CN105553442A - Network-based H-infinity filter information processing method for Lipschitz nonlinear system - Google Patents

Abstract

The invention discloses a network-based H-infinity filter information processing method for a Lipschitz nonlinear system. The method comprises the steps of: 1) analyzing a networked Lipschitz nonlinear system interfered by noise whose statistical characteristics are difficult to determine; and performing quantization processing on a measuring output and an estimated signal of the system and transmitting the measuring output and the estimated signal to the filter over the network; 2) after the filter receives the data, separating the measuring output and the estimated signal; and discussing issues of the H-infinity filter for the Lipschitz nonlinear system based on the data transfer process described by the Markov chain; and 3) establishing a new networked Lipschitz nonlinear system and a filter model based on the state transfer probability information of the Markov chain, and estimating the system state based on the newly established filter model. According to the invention, issues, including quantization and packet loss, in the design of H-infinity filters for Lipschitz nonlinear systems are studied, an information processing method based on the filter is provided, and estimation of the filter for the system state is achieved.

Description

The H of network Lipschitz non linear system ∞filter information processing method

Technical field

The present invention relates to a kind of network control system, especially relate to the H of network Lipschitz non linear system _∞filter information processing method.

Background technology

Along with the development of network technology, communication network application is in the controls more and more extensive.This control system by communication network formation closed loop is called network control system or network control system.In network control system, transducer, controller and actuator utilize network to carry out information exchange, therefore, network control system have convenient for installation and maintenance, flexibility is high and can realize the advantages such as Long-distance Control.

Because network control system introduces communication network in control loop, therefore create the problems such as data quantification and data-bag lost.If when the state of networked system can not be surveyed and be subject to noise disturbance, the state of designing filter to system is needed to estimate.When the noise be subject to by estimating system is white noise, can designs and adopt estimation error variance to estimate system mode as the Kalman filter of performance metric and linear filter.

At present, network design of filter mainly linear system, there is fan-shaped nonlinear system to unify the non linear system described by T-S fuzzy model.Lipschitz non linear system is the important non linear system of a class, such as, the robot system that there is trigonometric function item is Lipschitz non linear system, and the non linear system of some complexity can be described as linear system and the nonlinear terms sum meeting Lipschitz condition.But existing network design of filter Problems existing has: one, by estimated signal by wire instead of by Internet Transmission to long-range filter, the system of adding realizes cost, is unfavorable for system installation and maintenance.Two, main consideration network transfer delay and data-bag lost, and make great efforts distribution data of description transmitting procedure with shellfish, be not suitable for the situation of data by wireless network transmissions.Therefore, when Lipschitz non linear system be subject to statistical property be difficult to the noise disturbance determined time, measurement exports and is undertaken quantizing by estimated signal and by Internet Transmission to long-range filter by the present invention, and by Markov chain data of description transmitting procedure, devises network H _∞filter.

Summary of the invention

The object of the invention is the deficiency existed for prior art, propose a kind of H of network Lipschitz non linear system _∞filter information processing method.

The technical scheme that the present invention takes is as follows:

The H of network Lipschitz non linear system _∞filter information processing method, comprises the steps:

1) first the networking Lipschitz non linear system being subject to the noise jamming that statistical property is difficult to determine is analyzed; And the measurement of system is exported and carried out quantification treatment by estimated signal, be sent to filter end by network;

2) after filter receives data, measurement is exported and be separated with by estimated signal; And based on the data transmission procedure that Markov chain describes, the H of Lipschitz non linear system is discussed _∞filter problem;

3) based on the state transition probability information of Markov chain, set up novel networking Lipschitz non linear system and filter model, and estimate according to the state of newly-established filter model to system.

Described step 1) in, the state equation that Lipschitz non linear system is set up is as follows

x(k+1)＝Ax(k)+Ff(k,x(k))+Bw(k)

y(k)＝Cx(k)+Gg(k,x(k))+Dw(k)(1)

z(k)＝Lx(k)

Wherein: x (k) ∈ R ⁿstate vector, y (k) ∈ R ^pmeasure to export, z (k) ∈ R ^qby estimated signal, w (k) ∈ R ^mspace L ₂[0, ∞) on noise signal, A, F, B, C, G, D and L are the coefficient matrixes of known corresponding dimension, f (k, x (k)) and g (k, x (k)) be the Nonlinear Vector function of satisfied following Lipschitz condition: f (k, 0)=0, g (k, 0)=0, || f (k, x (k)) ||≤|| F ₁x (k) ||, || g (k, x (k)) ||≤|| G ₁x (k) ||, wherein F ₁, G ₁it is known respective dimension matrix number.

Described step 1) in, the measurement of system to be exported and carried out the method for quantification treatment by estimated signal specific as follows:

Measure and export y (k) and after quantizing, broken into a packet by Internet Transmission to filter node by the element of estimated signal z (k), first quantize it before transmission, quantizer is:

$Q\left(v\right)=\left\{\begin{array}{cc}{u}_i,& \frac{1}{1+\mathrm{\&delta;}}{u}_i<v\&le;\frac{1}{1-\mathrm{\&delta;}}{u}_i,v>0\\ 0,& v=0\\ -Q(-v),& v<0\end{array}\right.---\left(2\right)$

Wherein, the quantization level collection U={ ± u of system _i, u _i=ρ ⁱu ₀, i=± 1, ± 2 ... ∪ { ± u ₀∪ { 0}, 0< ρ <1, u ₀>0, ρ is the quantization resolution of quantizer Q (v).

Described step 2) in, the data transmission procedure method that Markov chain describes is as follows:

σ (k)=0 represents that data are not lost by during Internet Transmission; σ (k)=1 represents that data are lost by producing during Internet Transmission; State transition probability matrix P=[the p of Markov chain _ij], wherein p _ij>=0, work as p ₀₁+ p ₁₀when=1, transmitting procedure for shellfish make great efforts distribution;

When data are by network normal transmission, then after filter receives data, measurement exported and be separated with by estimated signal; Filter input y _f(k)=Q (y (k)), filter receive by estimated signal z _c(k)=Q (z (k)); The quantizer of system adopts logarithmic quantization device, therefore y _f(k)=(I+H (k)) y (k), z _c(k)=(I+H (k)) z (k), wherein I is the unit matrix of corresponding dimension, and H (k) is uncertain matrix, and meets || H (k) ||≤δ;

When data occur to lose in transmitting procedure, filter does not receive the measurement that network transmits and exports and by estimated signal, now suppose that filter input keeps the value of previous moment constant, i.e. y _f(k)=y _f(k-1), filter does not receive by estimated signal, i.e. z _c(k)=0, what such filter inputted and received can be turned to by estimated signal:

y _f(k)＝(1-σ(k))(I+H(k))y(k)+σ(k)y _f(k-1)(3)

z _c(k)＝(1-σ(k))(I+H(k))z(k)(4)。

Described step 2) H of Lipschitz non linear system is discussed _∞the method of filter problem is specific as follows:

For output z (k) of estimator (1), design the pattern-dependent filter of following form:

x _f(k+1)＝A _fσ(k)x _f(k)+B _fσ(k)y _f(k)

(5)

z _f(k)＝C _fσ(k)x _f(k)

Wherein: x _f(k) ∈ R ⁿfilter status vector, y _f(k) ∈ R ^pfilter input, z _f(k) ∈ R ^qestimated signal, A _{f σ (k)}, B _{f σ (k)}and C _{f σ (k)}, { 0,1} is filter parameter undetermined to σ (k)=i ∈;

Definition vector $\tilde{x}\left(k\right)={\left[\begin{array}{ccc}{x}^T\left(k\right)& x_f^T\left(k\right)& y_f^T\left(k\right)\end{array}\right]}^T,$ η (k)=[f ^t(k, x (k)) g ^t(k, x (k))] ^t, evaluated error e (k)=z _c(k)-z _fk (), by formula (1), formula (3), formula (4) and formula (5), can obtain following filtering error system:

$\begin{array}{c}\tilde{x}(k+1)={\tilde{A}}_{\mathrm{\&sigma;}\left(k\right)}\tilde{x}\left(k\right)+{\tilde{F}}_{\mathrm{\&sigma;}\left(k\right)}\mathrm{\&eta;}\left(k\right)+{\tilde{B}}_{\mathrm{\&sigma;}\left(k\right)}w\left(k\right)\\ e\left(k\right)={\tilde{C}}_{\mathrm{\&sigma;}\left(k\right)}\tilde{x}\left(k\right)\end{array},\mathrm{\&sigma;}\left(k\right)=i\&Element;\{0,1\}---\left(6\right)$

Wherein: ${\tilde{A}}_0={\hat{A}}_0+\hat{D}H\left(k\right)E_1,{\tilde{F}}_0={\hat{F}}_0+\hat{D}H\left(k\right)E_2,{\tilde{B}}_0={\hat{B}}_0+\hat{D}H\left(k\right)E_3,{\tilde{C}}_0=\hat{C}+H\left(k\right)E_4,$ ${\hat{A}}_0=\left[\begin{array}{ccc}A& 0& 0\\ B_{f0}& A_{f0}& 0\\ C& 0& 0\end{array}\right],{\hat{F}}_0=\left[\begin{array}{cc}F& 0\\ 0& B_{f0}G\\ 0& G\end{array}\right],{\hat{B}}_0=\left[\begin{array}{c}B\\ B_{f0}D\\ D\end{array}\right],\hat{D}=\left[\begin{array}{c}0\\ B_{f0}\\ I\end{array}\right],$ E ₁＝[C00]，E ₂＝[0G]，E ₃＝D， $\hat{C}=\left[\begin{array}{cc}L-C_{f0}& 0\end{array}\right],$ E ₄＝[L00]， $\begin{array}{cc}{\tilde{A}}_1=\left[\begin{array}{ccc}A& 0& 0\\ 0& A_{f1}& B_{f1}\\ 0& 0& I\end{array}\right],& {\tilde{F}}_1=\left[\begin{array}{cc}I& 0\\ 0& 0\\ 0& 0\end{array}\right]\end{array},$ $\begin{array}{cc}{\tilde{B}}_1=\left[\begin{array}{c}B\\ 0\\ 0\end{array}\right],& {\tilde{C}}_1=\left[\begin{array}{ccc}0& -C_{f1}& 0\end{array}\right]\end{array}.$

Described step 3), set up novel networking Lipschitz non linear system and filter model specific as follows:

For given positive number γ and quantization resolution ρ, if there is symmetric positive definite matrix P _i, M _i, R _iand matrix N _i, V _i, B _fi, i=0,1, positive scalar ε ₁, ε ₂and ε ₃, following linear MATRIX INEQUALITIES (7) and (8) are set up, then filtering error system (6) formula is Stochastic stable and has H _∞performance γ; Wherein filter parameter

$\left[\begin{array}{cccccccc}{\mathrm{\&Pi;}}_{11}& *& *& *& *& *& *& *\\ {\mathrm{\&Pi;}}_{21}& {\mathrm{\&Pi;}}_{22}& *& *& *& *& *& *\\ {\mathrm{\&Pi;}}_{31}& {\mathrm{\&Pi;}}_{32}& {\mathrm{\&Pi;}}_{\mathrm{33}}& *& *& *& *& *\\ {\mathrm{\&Pi;}}_{41}& {\mathrm{\&Pi;}}_{42}& {\mathrm{\&Pi;}}_{\mathrm{43}}& {\mathrm{\&Pi;}}_{\mathrm{44}}& *& *& *& *\\ {\mathrm{\&Pi;}}_{51}& {\mathrm{\&Pi;}}_{52}& {\mathrm{\&Pi;}}_{\mathrm{53}}& 0& {\mathrm{\&Pi;}}_{\mathrm{55}}& *& *& *\\ {\mathrm{\&Pi;}}_{61}& 0& 0& 0& 0& {\mathrm{\&Pi;}}_{\mathrm{66}}& *& *\\ 0& 0& 0& {\mathrm{\&Pi;}}_{\mathrm{74}}& {\mathrm{\&Pi;}}_{\mathrm{75}}& 0& {\mathrm{\&Pi;}}_{\mathrm{77}}& *\\ 0& 0& 0& 0& 0& {\mathrm{\&Pi;}}_{\mathrm{86}}& 0& {\mathrm{\&Pi;}}_{\mathrm{88}}\end{array}\right]<0---\left(7\right)$

$\left[\begin{array}{cccccc}{\mathrm{\&Omega;}}_{11}& *& *& *& *& *\\ 0& {\mathrm{\&Omega;}}_{22}& *& *& *& *\\ 0& 0& {\mathrm{\&Omega;}}_{33}& *& *& *\\ {\mathrm{\&Omega;}}_{41}& {\mathrm{\&Omega;}}_{42}& {\mathrm{\&Omega;}}_{43}& {\mathrm{\&Omega;}}_{44}& *& *\\ {\mathrm{\&Omega;}}_{51}& {\mathrm{\&Omega;}}_{52}& {\mathrm{\&Omega;}}_{53}& 0& {\mathrm{\&Omega;}}_{55}& *\\ {\mathrm{\&Omega;}}_{61}& 0& 0& 0& 0& {\mathrm{\&Omega;}}_{66}\end{array}\right]<0---\left(8\right)$

Wherein: ${\mathrm{\&Pi;}}_{11}=diag\left\{\begin{array}{ccc}-P_0+{\mathrm{\&epsiv;}}_1(F_1^T{F}_1+G_1^T{G}_1)+{\mathrm{\&epsiv;}}_2{\mathrm{\&delta;}}^2{C}^{T}C+{\mathrm{\&epsiv;}}_3{\mathrm{\&delta;}}^2{L}^{T}L,& -M_0,& -R_0\end{array}\right\},$

${\mathrm{\&Pi;}}_{21}=\left[\begin{array}{ccc}0& 0& 0\\ {\mathrm{\&epsiv;}}_2{\mathrm{\&delta;}}^2{G}^{T}C& 0& 0\end{array}\right],$ Π ₂₂＝diag{-ε ₁I,-ε ₁I+ε ₂δ ²G ^TG}，

Π ₃₁＝[ε ₂δ ²D ^TC00]，Π ₃₂＝[0ε ₂δ ²D ^TG]，Π ₃₃＝-γ ²I+ε ₂δ ²D ^TD，

$\begin{array}{ccc}{\mathrm{\&Pi;}}_{41}=\left[\begin{array}{ccc}{P}_{0}A& 0& 0\\ B_{f0}C& N_0& 0\\ R_{0}C& 0& 0\end{array}\right],& {\mathrm{\&Pi;}}_{42}=\left[\begin{array}{cc}{P}_{0}F& 0\\ 0& B_{f0}G\\ 0& R_{0}G\end{array}\right],& {\mathrm{\&Pi;}}_{43}=\left[\begin{array}{c}{P}_{0}B\\ B_{f0}D\\ R_{0}D\end{array}\right]\end{array},$

$\begin{array}{cc}{\mathrm{\&Pi;}}_{44}=diag\left\{\begin{array}{ccc}-p_{00}^{-1}{P}_0,& -p_{00}^{-1}{M}_0,& -p_{00}^{-1}{R}_0,\end{array}\right\},& {\mathrm{\&Pi;}}_{51}=\left[\begin{array}{ccc}{P}_{1}A& 0& 0\\ B_{f0}C& N_0& 0\\ R_{1}C& 0& 0\end{array}\right]\end{array},$

$\begin{array}{ccc}{\mathrm{\&Pi;}}_{52}=\left[\begin{array}{cc}{P}_{1}F& 0\\ 0& B_{f0}G\\ 0& R_{1}G\end{array}\right],& {\mathrm{\&Pi;}}_{53}=\left[\begin{array}{c}{P}_{1}B\\ B_{f0}D\\ R_{1}D\end{array}\right],& {\mathrm{\&Pi;}}_{55}=diag\left\{\begin{array}{ccc}-p_{01}^{-1}{P}_1,& -p_{01}^{-1}{M}_1,& -p_{01}^{-1}{R}_1\end{array}\right\},\end{array}$

Π ₆₁＝[L-V ₀0]，Π ₆₆＝-I， ${\mathrm{\&Pi;}}_{74}=\left[\begin{array}{ccc}0& B_{f0}^T& I\end{array}\right],$ Π ₇₅＝Π ₇₄，Π ₇₇＝-ε ₂I，

Π ₈₆＝I，Π ₈₈＝-ε ₃I， ${\mathrm{\&Omega;}}_{11}=diag\left\{\begin{array}{ccc}-P_1+{\mathrm{\&epsiv;}}_1(F_1^T{F}_1+G_1^T{G}_1),& -M_1,& -R_1\end{array}\right\},$ Ω ₂₂＝-ε ₁I，Ω ₃₃＝-γ ²I，

$\begin{array}{ccc}{\mathrm{\&Omega;}}_{41}=\left[\begin{array}{ccc}{P}_{0}A& 0& 0\\ 0& N_1& B_{f1}\\ 0& 0& R_0\end{array}\right],& {\mathrm{\&Omega;}}_{42}=\left[\begin{array}{cc}{P}_{0}F& 0\\ 0& 0\\ 0& 0\end{array}\right],& {\mathrm{\&Omega;}}_{43}=\left[\begin{array}{c}{P}_{0}B\\ 0\\ 0\end{array}\right]\end{array},$

$\begin{array}{cccc}{\mathrm{\&Omega;}}_{44}=diag\left\{\begin{array}{ccc}-p_{10}^{-1}{P}_0,& -p_{10}^{-1}{M}_0,& -p_{10}^{-1}{R}_0\end{array}\right\},& {\mathrm{\&Omega;}}_{51}=\left[\begin{array}{ccc}{P}_{1}A& 0& 0\\ 0& N_1& B_{f1}\\ 0& 0& R_1\end{array}\right],& {\mathrm{\&Omega;}}_{52}=\left[\begin{array}{cc}{P}_{1}F& 0\\ 0& 0\\ 0& 0\end{array}\right],& {\mathrm{\&Omega;}}_{53}=\left[\begin{array}{c}{P}_{1}B\\ 0\\ 0\end{array}\right]\end{array},$

${\mathrm{\&Omega;}}_{55}=diag\left\{\begin{array}{ccc}-p_{11}^{-1}{P}_1,& -p_{11}^{-1}{M}_1,& -p_{11}^{-1}{R}_1\end{array}\right\},$ Ω ₆₁＝[0-V ₁0]，Ω ₆₆＝-I。

Advantage of the present invention and remarkable result specific as follows:

(1) measurement of Lipschitz non linear system exported and undertaken quantizing by estimated signal and by Internet Transmission to long-range filter, devise network H _∞filter, compared to existing technology, what reduce filtering system realizes cost, improve convenience and the flexibility of system installation and maintenance, even if data are lost by existing in network transmission process, system is subject to the noise jamming that statistical property is difficult to determine, estimated signal also can be followed the tracks of by estimated signal preferably.

(2) the present invention adopts Markov chain data of description transmitting procedure, makes great efforts distribution data of description transmitting procedure and has more generality, be particularly useful for the situation of data by wireless network transmissions compared to employing shellfish.

(3) the present invention utilizes Lyapunov Functional Approach, have studied the H that a class has the Lipschitz non linear system of quantification and data-bag lost _∞filter design problem, and give the information processing method based on this filter, achieve the estimation of filter to system mode.

Accompanying drawing explanation

Fig. 1 is network non linear system filter structure figure;

Fig. 2 is data transmission procedure figure;

Fig. 3 is the drawing for estimate of filter to system mode.

Embodiment

Below in conjunction with accompanying drawing, technical scheme of the present invention is described in detail.

As shown in Figure 1, Figure 2 and Figure 3, be respectively network non linear system filter structure figure, data transmission procedure figure and filter to the drawing for estimate of system mode, the present invention is based on the H of the Lipschitz non linear system of network _∞filter information processing method, comprises the steps:

1) first the networking Lipschitz non linear system being subject to the noise jamming that statistical property is difficult to determine is analyzed; And the measurement of system is exported and carried out quantification treatment by estimated signal, be sent to filter end by network;

2) after filter receives data, measurement is exported and be separated with by estimated signal; And based on the data transmission procedure that Markov chain describes, the H of Lipschitz non linear system is discussed _∞filter problem;

3) based on the state transition probability information of Markov chain, set up novel networking Lipschitz non linear system and filter model, and estimate according to the state of newly-established filter model to system.

Wherein, step 1) in be subject to the noise jamming that statistical property is difficult to determine networking Lipschitz non linear system set up state equation such as formula (1).The measurement of system is exported and quantized by estimated signal and the method for process of pack as follows: measure and export y (k) and after quantification, broken into a packet by Internet Transmission to filter node by the element of estimated signal z (k).First quantize it before transmission, quantizer is formula (2).

Step 2) in Markov chain describe data transmission procedure method as follows: represent that data are not lost by during Internet Transmission with σ (k)=0; σ (k)=1 represents that data are lost by producing during Internet Transmission.State transition probability matrix P=[the p of Markov chain _ij], wherein $\begin{array}{cc}{p}_{ij}=\mathrm{Pr}\left\{\begin{array}{cc}\mathrm{\&sigma;}(k+1)=j|& \mathrm{\&sigma;}\left(k\right)=i\end{array}\right\}& \&ForAll;i,j\&Element;\{0,1\}\end{array},$ p _ij≥0， ${\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}=1.$ Work as p ₀₁+ p ₁₀when=1, transmitting procedure for shellfish make great efforts distribution, therefore have more generality with Markov chain data of description transmitting procedure, be especially applicable to data of description pass through wireless network transmissions situation.

When data are by network normal transmission, then after filter receives data, measurement exported and be separated with by estimated signal.Filter input y _f(k)=Q (y (k)), filter receive by estimated signal z _c(k)=Q (z (k)).Quantizer due to system have employed logarithmic quantization device, therefore y _f(k)=(I+H (k)) y (k), z _c(k)=(I+H (k)) z (k), wherein || H (k) ||≤δ.When data occur to lose in transmitting procedure, filter does not receive the measurement that network transmits and exports and by estimated signal, now suppose that filter input keeps the value of previous moment constant, i.e. y _f(k)=y _f(k-1), filter does not receive by estimated signal, i.e. z _c(k)=0.The formula (3) that can be turned to by estimated signal of such filter input and reception and formula (4)

For output z (k) of estimator (1), design the pattern-dependent filter such as formula (5).Definition vector $\tilde{x}\left(k\right)={\left[\begin{array}{ccc}{x}^T\left(k\right)& x_f^T\left(k\right)& y_f^T\left(k\right)\end{array}\right]}^T,$ η (k)=[f ^t(k, x (k)) g ^t(k, x (k))] ^t, evaluated error e (k)=z _c(k)-z _fk (), by formula (1), formula (3), formula (4) and formula (5), can obtain filtering error systematic (6).

Step 3) set up novel networking Lipschitz non linear system and filter model specific as follows: for given positive number γ and quantization resolution ρ, if there is symmetric positive definite matrix P _i, M _i, R _i, matrix N _i, V _i, B _fi, i=0,1, positive scalar ε ₁, ε ₂and ε ₃, LMI (7) and (8) are set up, then filtering error system (6) is Stochastic stable and has H _∞performance γ; Wherein filter parameter

The given matrix W with corresponding dimension of lemma, D and E, wherein W is symmetrical matrix.F is met for all ^tthe matrix F (k) of (k) F (k)≤I, W+DF (k) E+E ^tf ^t(k) D ^tthe necessary and sufficient condition that <0 sets up there is ε >0, makes W+ ε DD ^t+ ε ^-1e ^te<0.

Select following Lyapunov functional:

$\begin{array}{c}V\&lsqb;\tilde{x}\left(k\right),\mathrm{\&sigma;}\left(k\right)=i\&rsqb;={\tilde{x}}^T\left(k\right)S_i\tilde{x}\left(k\right)\\ =x^T\left(k\right)P_{i}x\left(k\right)+x_f^T\left(k\right)Q_i{x}_f\left(k\right)+y_f^T(k-1)R_i{y}_f(k-1)\end{array}$

When w (k)=0, difference along system (6) is:

$\begin{array}{c}\mathrm{\&Delta;}V\left(k\right)=E\{V\&lsqb;\tilde{x}(k+1),\mathrm{\&sigma;}(k+1)\&rsqb;|\tilde{x}\left(k\right),\mathrm{\&sigma;}\left(k\right)=i\}-V\&lsqb;\tilde{x}\left(k\right),\mathrm{\&sigma;}\left(k\right)=i\&rsqb;\\ ={\tilde{x}}^T(k+1){\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_i\tilde{x}(k+1)-{\tilde{x}}^T\left(k\right)S_i\tilde{x}\left(k\right)\\ ={\tilde{x}}^T\left(k\right){\tilde{A}}_i^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{A}}_i\tilde{x}\left(k\right)+2{\tilde{x}}^T\left(k\right){\tilde{A}}_i^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{F}}_i\mathrm{\&eta;}\left(k\right)\\ +{\mathrm{\&eta;}}^T\left(k\right){\tilde{F}}_i^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{F}}_i\mathrm{\&eta;}\left(k\right)-{\tilde{x}}^T\left(k\right)S_i\tilde{x}\left(k\right)\end{array}$

Due to

${\mathrm{\&eta;}}^T\left(k\right)\mathrm{\&eta;}\left(k\right)=f^T(k,x(k\left)\right)f(k,x(k\left)\right)+g^T(k,x(k\left)\right)g(k,x(k\left)\right)\&le;x^T\left(k\right)(F_1^T{F}_1+G_1^T{G}_1)x\left(k\right),$ So there is ε ₁>0, makes ${\mathrm{\&epsiv;}}_1{x}^T\left(k\right)(F_1^T{F}_1+G_1^T{G}_1)x\left(k\right)-{\mathrm{\&epsiv;}}_1{\mathrm{\&eta;}}^T\left(k\right)\mathrm{\&eta;}\left(k\right)\&GreaterEqual;0,$ Then

$\begin{array}{c}\mathrm{\&Delta;}V\left(k\right)\&le;{\tilde{x}}^T\left(k\right){\tilde{A}}_i^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{A}}_i\tilde{x}\left(k\right)+2{\tilde{x}}^T\left(k\right){\tilde{A}}_i^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{F}}_i\mathrm{\&eta;}\left(k\right)\\ +{\mathrm{\&eta;}}^T\left(k\right){\tilde{F}}_i^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{F}}_i\mathrm{\&eta;}\left(k\right)-{\tilde{x}}^T\left(k\right)S_i\tilde{x}\left(k\right)\\ +{\mathrm{\&epsiv;}}_1{x}^T\left(k\right)(F_1^T{F}_1+G_1^T{G}_1)x\left(k\right)-{\mathrm{\&epsiv;}}_1{\mathrm{\&eta;}}^T\left(k\right)\mathrm{\&eta;}\left(k\right)\\ ={\mathrm{\&xi;}}^T\left(k\right){\mathrm{\&Theta;}}_i\mathrm{\&xi;}\left(k\right)\end{array}$

Wherein $\begin{array}{cc}\mathrm{\&xi;}\left(k\right)={\left[\begin{array}{cc}{\tilde{x}}^T\left(k\right)& {\mathrm{\&eta;}}^T\left(k\right)\end{array}\right]}^T,& {\mathrm{\&Theta;}}_i=\left[\begin{array}{cc}{\tilde{A}}_i^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{A}}_i-S_i+W& {\tilde{A}}_i^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j\tilde{F}\\ {\tilde{F}}_i^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{A}}_i& {\tilde{F}}_i^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{F}}_i-{\mathrm{\&epsiv;}}_{1}I\end{array}\right]\end{array},$ $W={\left[\begin{array}{ccc}I& 0& 0\end{array}\right]}^T{\mathrm{\&epsiv;}}_1(F_1^T{F}_1+G_1^T{G}_1)\left[\begin{array}{ccc}I& 0& 0\end{array}\right].$

If n ₀=A _f0m ₀, V ₀=C _f0m ₀, N ₁=A _f1m ₁, V ₁=C _f1m ₁,

(7) formula both sides are multiplied by respectively $diag\{I,Q_0,I,I,I,I,P_0^{-1},I,R_0^{-1},P_1^{-1},I,R_1^{-1},I,I,I\}$ :

$\left[\begin{array}{cccccccc}-S_0+W+{\mathrm{\&epsiv;}}_2{\mathrm{\&delta;}}^2{E}_1^T{E}_1+{\mathrm{\&epsiv;}}_3{\mathrm{\&delta;}}^2{E}_4^T{E}_4& *& *& *& *& *& *& *\\ {\mathrm{\&epsiv;}}_2{\mathrm{\&delta;}}^2{E}_2^T{E}_1& -{\mathrm{\&epsiv;}}_{1}I+{\mathrm{\&epsiv;}}_2{\mathrm{\&delta;}}^2{E}_2^T{E}_2& *& *& *& *& *& *\\ {\mathrm{\&epsiv;}}_2{\mathrm{\&delta;}}^2{E}_3^T{E}_1& {\mathrm{\&epsiv;}}_2{\mathrm{\&delta;}}^2{E}_3^T{E}_2& -{\mathrm{\&gamma;}}^{2}I+{\mathrm{\&epsiv;}}_2{\mathrm{\&delta;}}^2{E}_3^T{E}_3& *& *& *& *& *\\ {\hat{A}}_0& {\hat{F}}_0& {\hat{B}}_0& -p_{00}^{-1}{S}_0^{-1}& *& *& *& *\\ {\hat{A}}_0& {\hat{F}}_0& {\hat{B}}_0& 0& -p_{01}^{-1}{S}_1^{-1}& *& *& *\\ \hat{C}& 0& 0& 0& 0& -I& *& *\\ 0& 0& 0& {\hat{D}}^T& {\hat{D}}^T& 0& -{\mathrm{\&epsiv;}}_{2}I& *\\ 0& 0& 0& 0& 0& I& 0& -{\mathrm{\&epsiv;}}_{3}I\end{array}\right]<0$

Namely

$\left[\begin{array}{ccccccc}-S_0+W+{\mathrm{\&epsiv;}}_2{\mathrm{\&delta;}}^2{E}_1^T{E}_1& *& *& *& *& *& *\\ {\mathrm{\&epsiv;}}_2{\mathrm{\&delta;}}^2{E}_2^T{E}_1& -{\mathrm{\&epsiv;}}_{1}I+{\mathrm{\&epsiv;}}_2{\mathrm{\&delta;}}^2{E}_2^T{E}_2& *& *& *& *& *\\ {\mathrm{\&epsiv;}}_2{\mathrm{\&delta;}}^2{E}_3^T{E}_1& {\mathrm{\&epsiv;}}_2{\mathrm{\&delta;}}^2{E}_3^T{E}_2& -{\mathrm{\&gamma;}}^{2}I+{\mathrm{\&epsiv;}}_2{\mathrm{\&delta;}}^2{E}_3^T{E}_3& *& *& *& *\\ {\hat{A}}_0& {\hat{F}}_0& {\hat{B}}_0& -p_{00}^{-1}{S}_0^{-1}& *& *& *\\ {\hat{A}}_0& {\hat{F}}_0& {\hat{B}}_0& 0& -p_{01}^{-1}{S}_1^{-1}& *& *\\ \hat{C}& 0& 0& 0& 0& -I& *\\ 0& 0& 0& {\hat{D}}^T& {\hat{D}}^T& 0& -{\mathrm{\&epsiv;}}_{3}I\end{array}\right]$

$+{\mathrm{\&epsiv;}}_3^{-1}\left[\begin{array}{c}0\\ 0\\ 0\\ 0\\ 0\\ I\\ 0\end{array}\right]\left[\begin{array}{ccccccc}0& 0& 0& 0& 0& I& 0\end{array}\right]+{\mathrm{\&epsiv;}}_3{\mathrm{\&delta;}}^2\left[\begin{array}{c}{E}_4^T\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\end{array}\right]\left[\begin{array}{ccccccc}{E}_4& 0& 0& 0& 0& 0& 0\end{array}\right]<0$

Will substitute into, according to lemma, above formula can turn to:

$\left[\begin{array}{ccccccc}-S_0+W+{\mathrm{\&epsiv;}}_2{\mathrm{\&delta;}}^2{E}_1^T{E}_1& *& *& *& *& *& *\\ {\mathrm{\&epsiv;}}_2{\mathrm{\&delta;}}^2{E}_2^T{E}_1& -{\mathrm{\&epsiv;}}_{1}I+{\mathrm{\&epsiv;}}_2{\mathrm{\&delta;}}^2{E}_2^T{E}_2& *& *& *& *& *\\ {\mathrm{\&epsiv;}}_2{\mathrm{\&delta;}}^2{E}_3^T{E}_1& {\mathrm{\&epsiv;}}_2{\mathrm{\&delta;}}^2{E}_3^T{E}_2& -{\mathrm{\&gamma;}}^{2}I+{\mathrm{\&epsiv;}}_2{\mathrm{\&delta;}}^2{E}_3^T{E}_3& *& *& *& *\\ {\hat{A}}_0& {\hat{F}}_0& {\hat{B}}_0& -p_{00}^{-1}{S}_0^{-1}& *& *& *\\ {\hat{A}}_0& {\hat{F}}_0& {\hat{B}}_0& 0& -p_{01}^{-1}{S}_1^{-1}& *& *\\ {\hat{C}}_0& 0& 0& 0& 0& -I& *\\ 0& 0& 0& {\hat{D}}^T& {\hat{D}}^T& 0& -{\mathrm{\&epsiv;}}_{3}I\end{array}\right]<0$ Namely

$\left[\begin{array}{cccccc}-S_0+W& *& *& *& *& *\\ 0& -{\mathrm{\&epsiv;}}_{1}I& *& *& *& *\\ 0& 0& -{\mathrm{\&gamma;}}^{2}I& *& *& *\\ {\hat{A}}_0& {\hat{F}}_0& {\hat{B}}_0& -p_{00}^{-1}{S}_0^{-1}& *& *\\ {\hat{A}}_0& {\hat{F}}_0& {\hat{B}}_0& 0& -p_{01}^{-1}{S}_1^{-1}& *\\ {\hat{C}}_0& 0& 0& 0& 0& -I\end{array}\right]+{\mathrm{\&epsiv;}}_2^{-1}\left[\begin{array}{c}0\\ 0\\ 0\\ \hat{D}\\ \hat{D}\\ 0\end{array}\right]\left[\begin{array}{cccccc}0& 0& 0& {\hat{D}}^T& {\hat{D}}^T& 0\end{array}\right]$

$+{\mathrm{\&epsiv;}}_2{\mathrm{\&delta;}}^2\left[\begin{array}{c}{E}_1^T\\ E_2^T\\ E_3^T\\ 0\\ 0\\ 0\end{array}\right]\left[\begin{array}{cccccc}{E}_1& E_2& E_3& 0& 0& 0\end{array}\right]<0$

Will ${\tilde{A}}_0={\hat{A}}_0+\hat{D}H\left(k\right)E_1,{\tilde{F}}_0={\hat{F}}_0+\hat{D}H\left(k\right)E_2,{\tilde{B}}_0={\hat{B}}_0+\hat{D}H\left(k\right)E_3$ Substitute into, according to lemma, above formula can turn to:

$\left[\begin{array}{cccccc}-S_0+W& *& *& *& *& *\\ 0& -{\mathrm{\&epsiv;}}_{1}I& *& *& *& *\\ 0& 0& -{\mathrm{\&gamma;}}^{2}I& *& *& *\\ {\tilde{A}}_0& {\tilde{F}}_0& {\tilde{B}}_0& -p_{00}^{-1}{S}_0^{-1}& *& *\\ {\tilde{A}}_0& {\tilde{F}}_0& {\tilde{B}}_0& 0& -p_{01}^{-1}{S}_1^{-1}& *\\ {\tilde{C}}_0& 0& 0& 0& 0& -I\end{array}\right]<0$

Mend lemma by Schur, above formula can turn to:

$\begin{array}{c}{\mathrm{\&Xi;}}_0=\\ \left[\begin{array}{ccc}{\tilde{A}}_0^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{A}}_0-S_0+W+{\tilde{C}}_0^T{\tilde{C}}_0& *& *\\ {\tilde{F}}_0^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{A}}_0& {\tilde{F}}_0^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{F}}_0-{\mathrm{\&epsiv;}}_{1}I& *\\ {\tilde{F}}_0^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{A}}_0& {\tilde{B}}_0^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{F}}_0& {\tilde{B}}_0^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{B}}_0-{\mathrm{\&gamma;}}^{2}I\end{array}\right]<0\end{array}$

Can be obtained fom the above equation:

${\mathrm{\&Theta;}}_0=\left[\begin{array}{cc}{\tilde{A}}_0^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{A}}_0-S_0+W& *\\ {\tilde{F}}_0^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{A}}_0& {\tilde{F}}_0^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{A}}_0-{\mathrm{\&epsiv;}}_{1}I\end{array}\right]<0$

In like manner, by (8) Shi Ke get:

$\begin{array}{c}{\mathrm{\&Xi;}}_1=\\ \left[\begin{array}{ccc}{\tilde{A}}_1^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{A}}_1-S_1+W+{\tilde{C}}_1^T{\tilde{C}}_1& *& *\\ {\tilde{F}}_1^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{A}}_1& {\tilde{F}}_1^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{F}}_1-{\mathrm{\&epsiv;}}_{1}I& *\\ {\tilde{F}}_1^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{A}}_1& {\tilde{B}}_1^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{F}}_1& {\tilde{B}}_1^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{B}}_1-{\mathrm{\&gamma;}}^{2}I\end{array}\right]<0\end{array}$

Can obtain further:

${\mathrm{\&Theta;}}_1=\left[\begin{array}{cc}{\tilde{A}}_1^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{A}}_1-S_1+W& *\\ {\tilde{F}}_1^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{A}}_1& {\tilde{F}}_1^T{\mathrm{\&Sigma;}}_{j=0}^1{p}_{ij}{S}_j{\tilde{F}}_1-{\mathrm{\&epsiv;}}_{1}I\end{array}\right]<0.$

Therefore,

$E\{V\&lsqb;\tilde{x}(k+1),\mathrm{\&sigma;}(k+1)\&rsqb;|\tilde{x}\left(k\right),\mathrm{\&sigma;}\left(k\right)=i\}-V\&lsqb;\tilde{x}\left(k\right),\mathrm{\&sigma;}\left(k\right)=i\&rsqb;\&le;{\mathrm{\&xi;}}^T\left(k\right){\mathrm{\&Theta;}}_i\mathrm{\&xi;}\left(k\right)\&le;{\mathrm{\&beta;\&xi;}}^T\left(k\right)\mathrm{\&xi;}\left(k\right)<0$

Wherein for Θ _ieigenvalue of maximum.

When N >=1,

$E\{V\&lsqb;\tilde{x}(N+1),\mathrm{\&sigma;}(N+1)\&rsqb;\}-V({\tilde{x}}_0,{\mathrm{\&sigma;}}_0)\&le;{\mathrm{\&Sigma;}}_{k=0}^N\mathrm{\&beta;}E\&lsqb;{\mathrm{\&xi;}}^T\left(k\right)\mathrm{\&xi;}\left(k\right)\&rsqb;\&le;{\mathrm{\&Sigma;}}_{k=0}^N\mathrm{\&beta;}E\&lsqb;{\tilde{x}}^T\left(k\right)\tilde{x}\left(k\right)\&rsqb;$

Above formula can turn to:

${\mathrm{\&Sigma;}}_{k=0}^{N}E\&lsqb;{\tilde{x}}^T\left(k\right)\tilde{x}\left(k\right)\&rsqb;\&le;{\mathrm{\&beta;}}^{-1}E\{V\&lsqb;\tilde{x}(N+1),\mathrm{\&sigma;}(N+1)\&rsqb;\}-{\mathrm{\&beta;}}^{-1}V({\tilde{x}}_0,{\mathrm{\&sigma;}}_0)$

As N → ∞, can obtain:

${\mathrm{\&Sigma;}}_{k=0}^{\mathrm{\&infin;}}E\&lsqb;{\tilde{x}}^T\left(k\right)\tilde{x}\left(k\right)\&rsqb;<-{\mathrm{\&beta;}}^{-1}V({\tilde{x}}_0,{\mathrm{\&sigma;}}_0)<\mathrm{\&infin;}$

Therefore, filtering error system (6) is Stochastic stable.

Prove that filtering error system (6) has H below _∞performance γ.Under zero initial condition, definition

$J_N=E\{{\mathrm{\&Sigma;}}_{k=0}^N\&lsqb;e^T\left(k\right)e\left(k\right)-{\mathrm{\&gamma;}}^2{w}^T\left(k\right)w\left(k\right)\&rsqb;\}$

Above formula can be expressed as:

Wherein

As N → ∞, can obtain:

$J_{\mathrm{\&infin;}}=E\{\underset{k=0}{\overset{\mathrm{\&infin;}}{\&Sigma;}}\&lsqb;z^T\left(k\right)z\left(k\right)-{\mathrm{\&gamma;}}^2{w}^T\left(k\right)w\left(k\right)\&rsqb;\}<0$

Therefore, filtering error system (6) has H _∞performance γ.

Below according to example, verify validity of the present invention and superiority.

In FIG, the such as Lipschitz non linear system shown in formula (1), parameter is as follows:

$\begin{array}{ccc}A=\left[\begin{array}{cc}0.2& 0.3\\ 0.1& 0.1\end{array}\right],& F=\left[\begin{array}{cc}0.3& 0.4\\ 0.4& 0.2\end{array}\right],& B=\left[\begin{array}{c}0.4\\ 0.1\end{array}\right]\end{array},$ C=[0.10.1], G=[0.10.2], D=0.3, L=[11], nonlinear function f (k, x (k))=0.1sin (x (k)), g (k, x (k))=0.1sin (x (k)), quantization resolution ρ=0.5 of quantizer Q (v), H _∞performance γ=1.8, data transmission procedure is as shown in Figure 2, its state transition probability matrix $P=\left[\begin{array}{cc}0.8& 0.2\\ 0.7& 0.3\end{array}\right],$ Noise signal $w\left(k\right)=\left\{\begin{array}{cc}0.5,& 5<k\&le;15\\ -0.5,& 55<k\&le;65\\ 0,& otherwise\end{array}\right..$

Utilize the LMI tool box in MATLAB to solve LMI formula (7) and formula (8) filter parameter can be obtained be:

$\begin{array}{cc}{A}_{f0}=\left[\begin{array}{cc}0.1106& 0.3278\\ 0.1357& 0.4021\end{array}\right],& B_{f0}=\left[\begin{array}{c}2.6164\\ 4.6841\end{array}\right]\end{array},$ C _f0＝[0.10130.1001]，

$\begin{array}{cc}{A}_{f1}=\left[\begin{array}{cc}0.1203& 0.0319\\ 0.1583& 0.2794\end{array}\right],& B_{f1}=\left[\begin{array}{c}4.8483\\ 8.8104\end{array}\right]\end{array},$ C _f1＝[0.11950.0962]。

Claims (6)

1. the H of network Lipschitz non linear system _∞filter information processing method, is characterized in that, comprises the steps:

1) first the networking Lipschitz non linear system being subject to the noise jamming that statistical property is difficult to determine is analyzed; And the measurement of system is exported and carried out quantification treatment by estimated signal, be sent to filter end by network;

2) after filter receives data, measurement is exported and be separated with by estimated signal; And based on the data transmission procedure that Markov chain describes, the H of Lipschitz non linear system is discussed _∞filter problem;

3) based on the state transition probability information of Markov chain, set up novel networking Lipschitz non linear system and filter model, and estimate according to the state of newly-established filter model to system.

2. the H of network Lipschitz non linear system according to claim 1 _∞design of filter, is characterized in that, described step 1) in, the state equation that Lipschitz non linear system is set up is as follows

x(k+1)＝Ax(k)+Ff(k,x(k))+Bw(k)

y(k)＝Cx(k)+Gg(k,x(k))+Dw(k)(1)

z(k)＝Lx(k)

Wherein: x (k) ∈ R ⁿstate vector, y (k) ∈ R ^pmeasure to export, z (k) ∈ R ^qby estimated signal, w (k) ∈ R ^mspace L ₂[0, ∞) on noise signal, A, F, B, C, G, D and L are the coefficient matrixes of known corresponding dimension, f (k, x (k)) and g (k, x (k)) be the Nonlinear Vector function of satisfied following Lipschitz condition: f (k, 0)=0, g (k, 0)=0, || f (k, x (k)) ||≤|| F ₁x (k) ||, || g (k, x (k)) ||≤|| G ₁x (k) ||, wherein F ₁, G ₁it is known respective dimension matrix number.

3. the H of network Lipschitz non linear system according to claim 2 _∞design of filter, is characterized in that, described step 1) in, the measurement of system to be exported and carried out the method for quantification treatment by estimated signal specific as follows:

Measure and export y (k) and after quantizing, broken into a packet by Internet Transmission to filter node by the element of estimated signal z (k), first quantize it before transmission, quantizer is:

$Q\left(v\right)=\left\{\begin{array}{cc}{u}_i,& \frac{1}{1+\mathrm{\&delta;}}{u}_i<v\&le;\frac{1}{1-\mathrm{\&delta;}}{u}_i,v>0\\ 0,& v=0\\ -Q(-v),& v<0\end{array}\right.---\left(2\right)$

Wherein, the quantization level collection U={ ± u of system _i, u _i=ρ ⁱu ₀, i=± 1, ± 2 ... ∪ { ± u ₀∪ { 0}, 0< ρ <1, u ₀>0, ρ is the quantization resolution of quantizer Q (v).

4. the H of network Lipschitz non linear system according to claim 3 _∞design of filter, is characterized in that, described step 2) in, the data transmission procedure method that Markov chain describes is as follows:

σ (k)=0 represents that data are not lost by during Internet Transmission; σ (k)=1 represents that data are lost by producing during Internet Transmission; State transition probability matrix P=[the p of Markov chain _ij], wherein $p_{ij}=\mathrm{Pr}\{\mathrm{\&sigma;}(k+1)=j|\mathrm{\&sigma;}\left(k\right)=i\}\&ForAll;i,j\&Element;\{0,1\},$ P _ij>=0, work as p ₀₁+ p ₁₀when=1, transmitting procedure for shellfish make great efforts distribution;

When data are by network normal transmission, then after filter receives data, measurement exported and be separated with by estimated signal; Filter input y _f(k)=Q (y (k)), filter receive by estimated signal z _c(k)=Q (z (k)); The quantizer of system adopts logarithmic quantization device, therefore y _f(k)=(I+H (k)) y (k), z _c(k)=(I+H (k)) z (k), wherein I is the unit matrix of corresponding dimension, and H (k) is uncertain matrix, and meets || H (k) ||≤δ;

When data occur to lose in transmitting procedure, filter does not receive the measurement that network transmits and exports and by estimated signal, now suppose that filter input keeps the value of previous moment constant, i.e. y _f(k)=y _f(k-1), filter does not receive by estimated signal, i.e. z _c(k)=0, what such filter inputted and received can be turned to by estimated signal:

y _f(k)＝(1-σ(k))(I+H(k))y(k)+σ(k)y _f(k-1)(3)

z _c(k)＝(1-σ(k))(I+H(k))z(k)(4)。

5. the H of network Lipschitz non linear system according to claim 4 _∞design of filter, is characterized in that, described step 2) H of Lipschitz non linear system is discussed _∞the method of filter problem is specific as follows:

For output z (k) of estimator (1), design the pattern-dependent filter of following form:

x _f(k+1)＝A _fσ(k)x _f(k)+B _fσ(k)y _f(k)

z _f(k)＝C _fσ(k)x _f(k)(5)

Wherein: x _f(k) ∈ R ⁿfilter status vector, y _f(k) ∈ R ^pfilter input, z _f(k) ∈ R ^qestimated signal, A _{f σ (k)}, B _{f σ (k)}and C _{f σ (k)}, { 0,1} is filter parameter undetermined to σ (k)=i ∈;

Definition vector $\tilde{x}\left(k\right)={\left[\begin{array}{ccc}{x}^T\left(k\right)& x_f^T\left(k\right)& y_f^T\left(k\right)\end{array}\right]}^T,\mathrm{\&eta;}\left(k\right)={\left[\begin{array}{cc}{f}^T(k,x(k\left)\right)& g^T(k,x(k\left)\right)\end{array}\right]}^T,$ Evaluated error e (k)=z _c(k)-z _fk (), by formula (1), formula (3), formula (4) and formula (5), can obtain following filtering error system:

$\begin{array}{c}\tilde{x}(k+1)={\tilde{A}}_{\mathrm{\&sigma;}\left(k\right)}\tilde{x}\left(k\right)+{\tilde{F}}_{\mathrm{\&sigma;}\left(k\right)}\mathrm{\&eta;}\left(k\right)+{\tilde{B}}_{\mathrm{\&sigma;}\left(k\right)}w\left(k\right)\\ e\left(k\right)={\tilde{C}}_{\mathrm{\&sigma;}\left(k\right)}\tilde{x}\left(k\right)\end{array},\mathrm{\&sigma;}\left(k\right)=i\&Element;\{0,1\}---\left(6\right)$

Wherein: ${\tilde{A}}_0={\hat{A}}_0+\hat{D}H\left(k\right)E_1,{\tilde{F}}_0={\hat{F}}_0+\hat{D}H\left(k\right)E_2,{\tilde{B}}_0={\hat{B}}_0+\hat{D}H\left(k\right)E_3,{\tilde{C}}_0=\hat{C}+H\left(k\right)E_4,$

${\hat{A}}_0=\left[\begin{array}{ccc}A& 0& 0\\ B_{f0}& A_{f0}& 0\\ C& 0& 0\end{array}\right],{\hat{F}}_0=\left[\begin{array}{cc}F& 0\\ 0& B_{f0}G\\ 0& G\end{array}\right],{\hat{B}}_0=\left[\begin{array}{c}B\\ B_{f0}D\\ D\end{array}\right],\hat{D}=\left[\begin{array}{c}0\\ B_{f0}\\ I\end{array}\right],$ E ₁＝[C00]，

E ₂＝[0G]，E ₃＝D， $\hat{C}=\left[\begin{array}{ccc}L& -C_{f0}& 0\end{array}\right],$ E ₄＝[L00]， ${\tilde{A}}_1=\left[\begin{array}{ccc}A& 0& 0\\ 0& A_{f1}& B_{f1}\\ 0& 0& I\end{array}\right],{\tilde{F}}_1=\left[\begin{array}{cc}I& 0\\ 0& 0\\ 0& 0\end{array}\right],$

${\tilde{B}}_1=\left[\begin{array}{c}B\\ 0\\ 0\end{array}\right],{\hat{C}}_1=\left[\begin{array}{ccc}0& -C_{f1}& 0\end{array}\right].$

6. the H of network Lipschitz non linear system according to claim 5 _∞design of filter, is characterized in that, described step 3), set up novel networking Lipschitz non linear system and filter model specific as follows:

For given positive number γ and quantization resolution ρ, if there is symmetric positive definite matrix P _i, M _i, R _iand matrix N _i, V _i, B _fi, i=0,1, positive scalar ε ₁, ε ₂and ε ₃, following linear MATRIX INEQUALITIES (7) and (8) are set up, then filtering error system (6) formula is Stochastic stable and has H _∞performance γ; Wherein filter parameter

$\left[\begin{array}{cccccccc}{\mathrm{\&Pi;}}_{11}& *& *& *& *& *& *& *\\ {\mathrm{\&Pi;}}_{21}& {\mathrm{\&Pi;}}_{\mathrm{22}}& *& *& *& *& *& *\\ {\mathrm{\&Pi;}}_{31}& {\mathrm{\&Pi;}}_{\mathrm{32}}& {\mathrm{\&Pi;}}_{\mathrm{33}}& *& *& *& *& *\\ {\mathrm{\&Pi;}}_{41}& {\mathrm{\&Pi;}}_{\mathrm{42}}& {\mathrm{\&Pi;}}_{\mathrm{43}}& {\mathrm{\&Pi;}}_{\mathrm{44}}& *& *& *& *\\ {\mathrm{\&Pi;}}_{51}& {\mathrm{\&Pi;}}_{\mathrm{52}}& {\mathrm{\&Pi;}}_{\mathrm{53}}& 0& {\mathrm{\&Pi;}}_{\mathrm{55}}& *& *& *\\ {\mathrm{\&Pi;}}_{61}& 0& 0& 0& 0& {\mathrm{\&Pi;}}_{\mathrm{66}}& *& *\\ 0& 0& 0& {\mathrm{\&Pi;}}_{\mathrm{74}}& {\mathrm{\&Pi;}}_{\mathrm{75}}& 0& {\mathrm{\&Pi;}}_{\mathrm{77}}& *\\ 0& 0& 0& 0& 0& {\mathrm{\&Pi;}}_{\mathrm{86}}& 0& {\mathrm{\&Pi;}}_{\mathrm{88}}\end{array}\right]<0---\left(7\right)$

$\left[\begin{array}{cccccc}{\mathrm{\&Omega;}}_{11}& *& *& *& *& *\\ 0& {\mathrm{\&Omega;}}_{22}& *& *& *& *\\ 0& 0& {\mathrm{\&Omega;}}_{33}& *& *& *\\ {\mathrm{\&Omega;}}_{41}& {\mathrm{\&Omega;}}_{42}& {\mathrm{\&Omega;}}_{43}& {\mathrm{\&Omega;}}_{44}& *& *\\ {\mathrm{\&Omega;}}_{51}& {\mathrm{\&Omega;}}_{52}& {\mathrm{\&Omega;}}_{53}& 0& {\mathrm{\&Omega;}}_{55}& *\\ {\mathrm{\&Omega;}}_{61}& 0& 0& 0& 0& {\mathrm{\&Omega;}}_{66}\end{array}\right]<0---\left(8\right)$

Wherein: ${\mathrm{\&Pi;}}_{11}=diag\left\{\begin{array}{ccc}-P_0+{\mathrm{\&epsiv;}}_1(F_1^T{F}_1+G_1^T{G}_1)+{\mathrm{\&epsiv;}}_2{\mathrm{\&delta;}}^2{C}^{T}C+{\mathrm{\&epsiv;}}_3{\mathrm{\&delta;}}^2{L}^{T}L,& -M_0,& -R_0\end{array}\right\},$

${\mathrm{\&Pi;}}_{21}=\left[\begin{array}{ccc}0& 0& 0\\ {\mathrm{\&epsiv;}}_2{\mathrm{\&delta;}}^2{G}^{T}C& 0& 0\end{array}\right],$ Π ₂₂＝diag{-ε ₁I,-ε ₁I+ε ₂δ ²G ^TG}，

Π ₃₁＝[ε ₂δ ²D ^TC00]，Π ₃₂＝[0ε ₂δ ²D ^TG]，Π ₃₃＝-γ ²I+ε ₂δ ²D ^TD，

${\mathrm{\&Pi;}}_{41}=\left[\begin{array}{ccc}{P}_{0}A& 0& 0\\ B_{f0}C& N_0& 0\\ R_{0}C& 0& 0\end{array}\right],{\mathrm{\&Pi;}}_{42}=\left[\begin{array}{cc}{P}_{0}F& 0\\ 0& B_{f0}G\\ 0& R_{0}G\end{array}\right],{\mathrm{\&Pi;}}_{43}=\left[\begin{array}{c}{P}_{0}B\\ B_{f0}D\\ R_{0}D\end{array}\right],$

${\mathrm{\&Pi;}}_{44}=diag\left\{\begin{array}{ccc}-p_{00}^{-1}{P}_0,& -p_{00}^{-1}{M}_0,& -p_{00}^{-1}{R}_0\end{array}\right\},{\mathrm{\&Pi;}}_{51}=\left[\begin{array}{ccc}{P}_{1}A& 0& 0\\ B_{f0}C& N_0& 0\\ R_{1}C& 0& 0\end{array}\right],$

${\mathrm{\&Pi;}}_{52}=\left[\begin{array}{cc}{P}_{1}F& 0\\ 0& B_{f0}G\\ 0& R_{1}G\end{array}\right],{\mathrm{\&Pi;}}_{53}=\left[\begin{array}{c}{P}_{1}B\\ B_{f0}D\\ R_{1}D\end{array}\right],{\mathrm{\&Pi;}}_{55}=diag\left\{\begin{array}{ccc}-p_{01}^{-1}{P}_1,& -p_{01}^{-1}{M}_1,& -p_{01}^{-1}{R}_1\end{array}\right\},$

Π ₆₁＝[L-V ₀0]，Π ₆₆＝-I， ${\mathrm{\&Pi;}}_{74}=\left[\begin{array}{ccc}0& B_{f0}^T& I\end{array}\right],$ Π ₇₅＝Π ₇₄，Π ₇₇＝-ε ₂I，

Π ₈₆＝I，Π ₈₈＝-ε ₃I， ${\mathrm{\&Omega;}}_{11}=diag\left\{\begin{array}{ccc}-P_1+{\mathrm{\&epsiv;}}_1(F_1^T{F}_1+G_1^T{G}_1),& -M_1,& -R_1\end{array}\right\},$ Ω ₂₂＝-ε ₁I，Ω ₃₃＝-γ ²I，

${\mathrm{\&Omega;}}_{41}=\left[\begin{array}{ccc}{P}_{0}A& 0& 0\\ 0& N_1& B_{f1}\\ 0& 0& R_0\end{array}\right],{\mathrm{\&Omega;}}_{42}=\left[\begin{array}{cc}{P}_{0}F& 0\\ 0& 0\\ 0& 0\end{array}\right],{\mathrm{\&Omega;}}_{43}=\left[\begin{array}{c}{P}_{0}B\\ 0\\ 0\end{array}\right],$

${\mathrm{\&Omega;}}_{44}=diag\left\{\begin{array}{ccc}-p_{10}^{-1}{P}_0,& -p_{10}^{-1}{M}_0,& -p_{10}^{-1}{R}_0\end{array}\right\},{\mathrm{\&Omega;}}_{51}=\left[\begin{array}{ccc}{P}_{1}A& 0& 0\\ 0& N_1& B_{f1}\\ 0& 0& R_1\end{array}\right],{\mathrm{\&Omega;}}_{52}=\left[\begin{array}{cc}{P}_{1}F& 0\\ 0& 0\\ 0& 0\end{array}\right],{\mathrm{\&Omega;}}_{53}=\left[\begin{array}{c}{P}_{1}B\\ 0\\ 0\end{array}\right],$

${\mathrm{\&Omega;}}_{55}=diag\left\{\begin{array}{ccc}-p_{11}^{-1}{P}_1,& -p_{11}^{-1}{M}_1,& -p_{11}^{-1}{R}_1\end{array}\right\},$ Ω ₆₁＝[0-V ₁0]，Ω ₆₆＝-I。