CN105589340A - Stability determination method of uncertain network multiple time delay system - Google Patents

Abstract

The present invention discloses a stability determination method of an uncertain network multiple time delay system. The method comprises: establishing a closed-loop network multiple time delay control system model, mapping the uncertainty of the closed-loop network multiple time delay control system to a convex polyhedron parameter space, and obtaining a convex polyhedron uncertain network multiple time delay control system model; performing determination to obtain the delay-dependent robust stability of the convex polyhedron uncertain network multiple time delay control system through a liberty matrix method on the basis of a construction Lyapunov function, and obtaining the sufficient condition of the delay-dependent robust stability. The stability determination method of an uncertain network multiple time delay system avoids that the same Lyapunov function is used for all the convex polyhedron vertexes in an uncertain space, and reduces the conservative property of the robust stability sufficient condition.

Description

A kind of stability judging method of uncertain network Systems with Multiple Time-Delays

Technical field

The invention belongs to automatic control technology field, relate to a kind of judgement of stability of uncertain network Systems with Multiple Time-DelaysMethod.

Background technology

Data volume that network control system need to be shared and exchange is increasing, type becomes increasingly complex, in actual workIn journey field, due to the limitation of human cognitive ability and method, and the complexity of objective things itself, be difficult to obtain systemDetermine or describe accurately, thereby causing a large amount of uncertainties to exist; While is along with the continuous expansion of modern control system scaleGreatly, complexity increases sharply, system architecture ambiguity, not modeling parameters ambiguity, external environment condition unpredictability, external disturbanceRandomness etc. further strengthened complexity and the source of system uncertain factor. The peace of modern control field to complication systemThe requirement of full property and reliability is more and more higher, the therefore uncertain factor of taking into account system, the robust control of research uncertain systemStrategy, to ensure that system dynamic characteristic still can keep better performance to have important theory meaning while variation in certain perturbation rangeJustice and more practical value.

In addition,, along with the development of mechanics of communication and complex network, large scale network networked control systems is low with its cost, connectionFlexibly, be easy to install the advantages such as expansion, maintenance is simple, function is complicated and become complex large system objective demand. But due to netThe feature of network to communication media time-sharing multiplex, in the time that multiple nodes carry out data interaction by network, usually occur data collision,Phenomenons such as information obstruction, disconnecting, multiframe transmission, thereby inevitably occur the non real-time transmission of information, therefore exceptOutside the uncertainty of system, Time Delay is the another subject matter facing in network control system research, and it oftenCause the major reason of system performance degradation.

Uncertainty at descriptive system adopts norm-bounded ambiguous model and convex polyhedron often; Wherein, norm hasBoundary's uncertainty description method, based on small gain theorem, has limited probabilistic Maximum tolerance, has certain officeSex-limited; The stability analysis of convex polyhedron uncertain system and robust Controller Design are mostly based on Lyapunov Quadratic StabilityTheoretical. But because Lyapunov Quadratic Stability concept is to using identical to all convex polyhedron summits in Instable SpaceLyapunov function, cause the conservative of result larger. Along with proposition and the LMI of parameter-dependent Lyapunov stability thoughtThe development of method is perfect, gradually this thinking is used for to the analysis and design to convex polyhedron uncertain control systems.

For the STUDY ON ROBUST CONTROL with the probabilistic discrete system of convex polyhedron, mainly contain following several side at presentMethod: (1) public Lyapunov function method, obtains discrete convex polyhedron to N convex polyhedron summit N LMI of structureThe criterion for robust stability of uncertain system, is converted into finite dimension problem by Infinite-dimensional problem. The method requires convex polyhedronEach summit is used a public Lypaunov matrix, therefore has larger conservative. (2) added martix structureLyapunov function method, by introducing added martix variable as the right of freedom tactical deployment of troops, remove in Lyapunov function matrix P (a) andSytem matrix A (a) product term, thus the conservative that system robust stable condition exists reduced. (3) Algebraic Structure structureLyapunov function method, by exploring the Algebraic Structure of Lyapunov stable condition of uncertain system parameter-dependent, then closesAnd similar terms, with require in multinomial each all positive definite ensure the robust stability of uncertain system. Based on this thinking instituteThe result obtaining is less than the result conservative based on Lyapunov Quadratic Stability theory, but most achievement in research allFor continuous system, also seldom relate to for the research of discrete system.

Summary of the invention

For above-mentioned problems of the prior art or defect, the object of the invention is to, a kind of uncertain net is providedThe stability judging method of network Systems with Multiple Time-Delays.

To achieve these goals, the present invention adopts following technical scheme:

A stability judging method for uncertain network Systems with Multiple Time-Delays, specifically comprises the following steps:

Step 1, sets up closed network multiple time delay control system model;

Step 2, is mapped to the uncertainty of closed network multiple time delay control system in convex polyhedron parameter space,To convex polyhedron uncertain network multiple time delay control system model;

Step 3, structure includes the Lyapunov function of multiple time delay information;

Step 4, utilizes right of freedom matrix method, the convex polyhedron uncertain network multiple time delay control that determining step 2 obtainsThe Robust Delay-Dependence Stability of system, obtains the relevant robust stability adequate condition of time lag; If meet the relevant robust stability of time lagAdequate condition, uncertain network Systems with Multiple Time-Delays is stable, if do not meet, uncertain network Systems with Multiple Time-Delays isUnsettled.

Particularly, the closed network multiple time delay control system model in described step 1 is:

Wherein,

Positive integerI=1,2,3 for time become time lag; A_p,B_p,C_pBe the real constant coefficient matrix of suitable dimension, k is current samplingMoment, x (k) ∈ RⁿFor the system state variables of augmentation, A_c,B_c,C_c,D_cIt is the real constant coefficient matrix of suitable dimension.

Particularly, the convex polyhedron uncertain network multiple time delay control system model in described step 2 is:

Wherein, A_0α,A_1α…,A_3αIt is sytem matrix group.

Particularly, in described step 3, the Lyapunov function that includes multiple time delay information of structure is as follows:

V(x(k))＝V₁+V₂+V₃+V₄

Wherein,

V₁＝x^T(k)P_αx(k)

In formula, P_α,R_1α,R_2α,R_3α∈R^n×nFor relying on parameter alpha_i(t) symmetric positive definite matrix, 0≤α_i(t)≤1，i＝1,2 ..., n is Bounded Real scalar function.

Particularly, the relevant robust of the time lag of the convex polyhedron uncertain network multiple time delay control system in described step 4Stable adequate condition is:

For time become time lagThere is symmetric positive definite matrix P_α＝P_α ^T>0，Q_α＝Q_α ^T>0，And the matrix N of arbitrarily suitable dimension_iα,M_iα,S_iα(i＝1,2)，X_α,Y_α,Z_α≥0Can make following one group of LMI set up:

Λ_23α＝d_maxΞ_23α

Λ_33α＝d_maxΞ_24α

Λ_34α＝d_maxΞ_34α

Ξ_ijα＝X_ijα+Y_ijα+Z_ijα，i，j＝1，2，3

Compared with prior art, the present invention has following technique effect:

1, the present invention is directed to data/address bus extensive use in control system, introduced unreliable the leading to that transmission time lag causesLetter factor and from internal system and outside uncertain factor, has completed system Multi Time Lag and uncertain from physical spaceTo the mapping of mathematical space, set up the uncertain networking of closed loop multiple time delay control system model.

2, the present invention is described and modeling the uncertainty of control system in three dimensions, by systematic uncertaintyBe mapped in convex polyhedron Instable Space, describe and compare with uncertain two-dimensional space, it is moving that describing method meets system moreStep response, can describe the uncertainty from system outside and system self structure flexibly, the uncertain institute of characterising parameterThe system obtaining describes to probabilistic Maximum tolerance ratio the conservative having still less with two-dimensional space.

3, the present invention adopts Lyapunov function method, and dynamical system Multi Time Lag packets of information is contained to the function into LyapunovIn. By having constructed an aobvious Lyapunov function containing time lag, according to Lyapunov Theory of Stability, based on the right of freedom tactical deployment of troopsStability to network control system is analyzed, and has avoided, in Instable Space, all convex polyhedron summits are used to phaseWith Lyapunov function, reduced the conservative of robust stability adequate condition.

4,, in Robust Delay-Dependence Stability decision method, by constructing the aobvious Lyapunov function containing time lag, and drawEnter added martix variable, offset the quadratic form integration item occurring in Lyapunov function difference, reduced the relevant Shandong of time lagRod is stablized the conservative of adequate condition.

Brief description of the drawings

Fig. 1 is closed network networked control systems Time-Delay model;

Fig. 2 works as d_max=9 o'clock convex polyhedron uncertain network networked control systems condition responsives;

Fig. 3 works as d_max=4 o'clock convex polyhedron uncertain network networked control systems condition responsives;

Fig. 4 works as d_max=9 o'clock deterministic network networked control systems are at the condition responsive on convex polyhedron summit 1;

Fig. 5 works as d_max=9 o'clock deterministic network networked control systems are at the condition responsive on convex polyhedron summit 2;

Fig. 6 works as d_max=9 o'clock deterministic network networked control systems are at the condition responsive on convex polyhedron summit 3;

Below in conjunction with the drawings and specific embodiments, the solution of the present invention is done and explained in further detail and illustrate.

Detailed description of the invention

Time lag characteristic to closed network networked control systems is analyzed, and the position distributing according to time lag is divided, can be byTime lag is divided into three parts: sampling transmission time lag τ_SC, control and calculate time lag τ_C, and control action time lag τ_CA, its generation positionDistribute as shown in Figure 1, now above-mentioned three part time lags analyzed:

(1) sampling transmission time lag τ_SC, sensor is to the transmission time lag of controller. In network control system, will passSensor samples sampled data and arrives being called during this period of time of controller " sensor-controller time lag ", is designated asK works asFront sampling instant,Be defined asWhereinWithRepresent that respectively controller starts s operation control signalMoment and sensor moment of starting sampling system output.

(2) control and calculate time lag τ_C, controller is carried out the calculating time lag that computing produces. In network control system, willController starts to calculate and has calculated controlled signal and be called during this period of time " controller calculating time lag ", is designated asK isCurrent sampling instant,Be defined asWhereinWithIt is controlled to be respectively that controller has calculatedThe moment of signal and the moment that starts calculating.

(3) control action time lag τ_CA, controller is to the transmission time lag of actuator. In network control system, will controlThe moment that device transmits control signal rises to what this signal was performed that device receives and is called during this period of time " controller-actuator time lag ",Be designated asK is current sampling instant,Be defined asWhereinWithRespectively that actuator receivesStart the moment of action and the moment that controller computing completes controlled signal to control signal.

Normally time, become, withWithCompare, its value is negligible, and rate of change is almostZero. In the time carrying out the analysis and synthesis of network control system, can start with its impact is reduced to minimum from hardware aspect, instituteWhat the network is guided time lag of introducing with ordinary circumstance control bus was often referred to is exactlyWithThese two kinds of time lags.

The stability judging method of uncertain network Systems with Multiple Time-Delays of the present invention, specifically comprises the following steps:

Step 1, sets up closed network multiple time delay control system model, and in this model process of establishing, taking into account system is not trueQualitative.

The structure chart of the closed network networked control systems based in Fig. 1, the discrete state equations that obtains controlled device is:

Wherein x_p∈RⁿRepresent the state vector of controlled device, u_p∈R^mRepresent input vector, y_p∈R^pRepresent output vector,K is current sampling instant; N, m, p represents respectively the dimension of controlled device in control system, actuator and sensor; A_p,B_p,C_pIt is the real constant coefficient matrix of suitable dimension.

The discrete state equations of controller can be by following the Representation Equation:

Wherein x_c∈RⁿRepresent the state vector of controller, u_c∈R^pRepresent the input vector of controller, y_c∈R^mRepresent controlThe output vector of device processed; N, p, m represents the dimension of controller, sensor and actuator; A_c,B_c,C_c,D_cThe reality that is suitable dimension is oftenMatrix number.

As shown in Figure 1, the analog-to-digital controlled device output vector of the process y that sensor collects_pThrough transmission channelAfter S-C, add sampling transmission time lag τ_SCInformation, as input vector u_cEnter controller; And the computing of process controllerDominant vector y_cAs output, after transmission channel C-A, add control action time lag τ_CAInformation, as input quantity, andAfter digital-to-analogue conversion, enter actuator.

DefinitionRepresent k the sampling transmission time lag τ between sampling period S-C_SC，Represent k sampling period C-ABetween control action time lag τ_CAThereby the time lag in network can be described by following relation:

Wherein,d_min,d_maxBe respectively minimum transfer time lag between node andMaximum transmitted time lag.

Introduce the system state variables vector of augmentationThe net based on time lag system theoryNetwork control system state equation can be expressed as:

Definition

Closed network multiple time delay control system can be write as:

Wherein

Can find out from above system model, the closed network multiple time delay control system that formula (6) represents is a bandConstant autonomous system while having the LINEAR CONTINUOUS of multiple time delay, can apply time lag system theory it is studied.

Step 2, the closed network multiple time delay control system model obtaining based on step 1, the system of further considering is not trueQualitative, the uncertainty of closed network multiple time delay control system is mapped in convex polyhedron parameter space, obtain protruding multiaspectBody uncertain network multiple time delay control system model.

The uncertain available following model representation of convex polyhedron:

Wherein, A_i∈R^n×mAnd A_di∈R^n×mFor known real matrix, uncertain parameter A and A_dBe bounded, belong to limitedThe convex combination of known matrix, A and A_dCan be expressed as:

S:＝{A₁,A₂,…,A_m,A_d1,A_d2,…,A_dn}∈Θ(8)

Wherein0≤α_i(t)≤1, i=1,2 ..., n is the real scalar function of bounded, andAnd meet:

Due to uncertain parameter alpha_i(t) may be time, become, also need to suppose that its rate of change is bounded, meet:

In formulaRepresent uncertain parameter alpha_i(t) rate of change.

From geometrically seeing uncertain parameter matrix A and A_dRespectively with A_iAnd A_diFor the convex polyhedron on summit; θ_i，i＝1 ..., m is the known scalar of determining.

Consider to have as follows the convex polyhedron uncertain network multiple time delay control system model of multiple case time lag:

Wherein x (k) ∈ RⁿFor the system state variables of augmentation, positive integerI=1,2,3 for time become time lag. Sytem matrixGroup (A_0α,A_1α,…,A_3α) uncertainty of descriptive system, it is convex combination collection bounded and that belong to limited known matrix:

$\mathrm{\Ψ}\stackrel{\mathrm{\Δ}}{=}\{{(A_0,A_1,\mathrm{...}{A}_3)}_{\mathrm{\α}}:{(A_0,A_1,\mathrm{...}{A}_3)}_{\mathrm{\α}}=\underset{i=1}{\overset{N}{\Σ}}{\mathrm{\α}}_i\left(t\right)(A_{0i},A_{1i},\mathrm{...}{A}_{3i}),\mathrm{\α}\∈N,q=3\}---\left(12\right)$

Wherein A_0i,A_1i,…,A_3i∈R^n×mFor known solid matrix. As can be seen from the above equation, any matrix of gathering Ψ that belongs to(A₀,A₁,…,A₃)_αCan be by N vertex matrix (A in set Ψ_0i,A_1i，…,A_3i), i=1 ..., the convex combination of N represents.0≤α in above formula_i(t)≤1, i=1,2 ..., n is Bounded Real scalar function, meets simultaneously:

Due to uncertain parameter alpha_i(t) may be time, become, also need to suppose that its rate of change is bounded, meet:

From geometrically seeing that uncertain parameter space is with A₀,A₁,A₂,A₃For the convex polyhedron on summit; θ_i, i=1 ..., m isThe known scalar of determining.

Convex polyhedron uncertainty description method can be described any convex polyhedron by defining uncertain parameter space,In actual modeling process, internal system and outside majority uncertainty can be convenient with the uncertain parameter model of convex polyhedronGround is described. Any norm-bounded is not in fact

Step 3, the convex polyhedron uncertain network multiple time delay control system model obtaining based on step 2, structure comprisesThere is the Lyapunov function of multiple time delay information.

The Lyapunov function of the convex polyhedron uncertain network multiple time delay control system shown in constructive formula (11):

V(x(k))＝V₁+V₂+V₃+V₄(15)

Wherein,

V₁＝x^T(k)P_αx(k)

In formula, P_α,R_1α,R_2α,R_3α∈R^n×nFor relying on parameter alpha_i(t) symmetric positive definite matrix.

For primary condition arbitrarily, along any track of system, the single order forward difference of Lyapunov function is:

Wherein,

To formula (18) application Schur complement fixed reason, known Λ < 0, is equivalent to:

Step 4, the Lyapunov function of constructing based on step 3, utilizes right of freedom matrix method, and it is protruding that determining step 2 obtainsThe Robust Delay-Dependence Stability of polyhedron uncertain network multiple time delay control system, obtains the relevant robust stability of time lag abundantCondition. If meet the relevant robust stability adequate condition of time lag, uncertain network Systems with Multiple Time-Delays is stable, if discontentedFoot, uncertain network Systems with Multiple Time-Delays is unsettled.

According to whether relevant to time lag information, the determination of stability side obtaining based on time lag system method for analyzing stabilityMethod and adequate condition can be divided into two classes: a class is On Delay-Dependent Stability condition, and a class is Delay-Independent Stability condition. ItsMiddle Delay-Independent Stability condition without any restriction, is not considered the size of time lag to time lag. Time lag don't-care condition is for arbitrarilyTime lag is all set up. Owing to not needing to know the relevant information of system time lag, Delay-Independent Stability method can be analyzed and processThe time lag of system the unknown. Under normal circumstances, the fairly simple and easily checking of the irrelevant conclusion of time lag. But for Small Time Lag orThe situation of person's time lag bounded, the irrelevant stable condition of time lag must bring larger conservative. Accordingly, On Delay-Dependent StabilityMethod is considered time lag information in the analysis of the stability of a system, has embodied the impact of time lag size on the stability of a system. LogicalOften, in time lag bounded or time lag, less in the situation that, On Delay-Dependent Stability condition has more than Delay-Independent Stability conditionLow conservative. Further, according to the information that whether comprises time lag derivative in stability condition, On Delay-Dependent Stability conditionCan be divided into again the relevant and time lag derivative relevant with time lag of the relevant and time lag derivative of time lag has nothing to do two kinds. Because time lag is relevant and time lagDerivative correlated condition has comprised more time lag information, thereby it has less conservative compared with the latter.

In order further to reduce conservative, the present invention is based on the convex polyhedron that right of freedom tactical deployment of troops determining step 2 obtains not trueDetermine the Robust Delay-Dependence Stability of networking Systems with Multiple Time-Delays model, obtain the relevant robust stability adequate condition of time lag.

First definition status x (l) forward difference is:

y(l)＝x(l+1)-x(l)(20)

Have following formula equation to set up:

The Lyapunov function of the convex polyhedron uncertain network Systems with Multiple Time-Delays shown in constructive formula (11):

V(k)＝V₁(k)+V₂(k)+V₃(k)+V₄(k)+V₅(k)(23)

V₁(k)＝x^T(k)P_αx(k)

Wherein P_α＝P_α ^T>0，Q_α＝Q_α ^T>0，For symmetric positive definite matrix undetermined, definitionLyapunov function single order forward difference Δ V (k)=V (k+1)-V (k), has:

ΔV₁(k)＝2x^T(k)P_αy(k)+y^T(k)P_αy(k)(25)

Meanwhile, utilize formula (22), for Arbitrary Matrix N_iα,M_iα,S_iα(i=1,2,3), have following null value equation to set up:

On the other hand, for the matrix X of any appropriate dimension, Y, Z >=0, has following null value equation to set up:

WhereinBy null value equation (30) and(31) the left side joins Δ V (k), and the single order forward difference Δ V (k) of Lyapunov function is further transformed to:

Wherein,According to LyapunovTheory of Stability, the relevant robust stability of time lag of the convex polyhedron uncertain network multiple time delay control system shown in formula (11)Adequate condition be Δ V (k) < 0 set up.

For time become time lagIf there is symmetric positive definite matrix P_α＝P_α ^T>0，Q_α＝Q_α ^T>0，And the matrix N of arbitrarily suitable dimension_iα,M_iα,S_iα(i＝1,2)，X_α,Y_α,Z_α≥0Following LMI is set up, and Δ V (k) < 0 sets up:

Wherein,

Λ_23α＝d_maxΞ_23α

Λ_24α＝d_maxΞ_24α

Λ_34α＝d_maxΞ_34α

Ξ_ijα＝X_ijα+Y_ijα+Z_ijα，i，j＝1，2，3

In other words, the relevant robust of the time lag of the convex polyhedron uncertain network multiple time delay control system shown in formula (11)Stable adequate condition is: for time become time lag There is symmetric positive definite matrix P_α＝P_α ^T>0，Q_α＝Q_α ^T>0，And the matrix N of arbitrarily suitable dimension_iα,M_iα,S_iα(i＝1,2)，X_α,Y_α,Z_α>=0 can make above-mentioned one group of LMI set up.

Embodiment:

Adopt the stability judging method of the uncertain network Systems with Multiple Time-Delays of the present invention's proposition, in given network time lagMinimum time lag border d_minTime, find the maximum time lag border of the network time lag of convex polyhedron uncertain network networked control systemsd_max, make to work asTime, closed network networked control systems is robust asymptotic stability. And forNetwork control system is at the determinacy case on three summits of convex polyhedron, when providing minimal network time lag border d_minTime, obtainThe maximum network time lag border d on three summits of convex polyhedron_max, and the result of several situations is compared. Concrete methods of realizingAs follows:

Step 1: controlled device is for having convex polyhedron uncertain network multiple time delay control system, its state-space modelFor:

Wherein, x (k) ∈ RⁿFor the system state variables of augmentation, positive integerI=1,2,3 for time become time lag. Matrix (A₀,A₁,…,A₃) be uncertain matrix group, belong to the uncertain set of convex polyhedron:

$\mathrm{\&Psi;}\stackrel{\mathrm{\&Delta;}}{=}\{{(A_0,A_1,\mathrm{...}{A}_3)}_{\mathrm{\&alpha;}}:{(A_0,A_1,\mathrm{...}{A}_3)}_{\mathrm{\&alpha;}}=\underset{i=1}{\overset{N}{\&Sigma;}}{\mathrm{\&alpha;}}_i\left(t\right)(A_{0i},A_{1i},\mathrm{...}{A}_{3i}),\mathrm{\&alpha;}\&Element;N,q=3\}---\left(40\right)$

Here establish α=3, gathering Ψ is 3 vertex matrix (A_0i,A_1i,…,A_3i), i=1,2,3 convex combination. Wherein:

Step 2, utilizes MatlabLMI tool box to solve, and works as d_min=6 o'clock, can be in the hope of convex polyhedron uncertain networkChange the maximum time lag border d of Systems with Multiple Time-Delays_max=9, and the solution of LMIs is:

Step 3, according to different minimum time lag border d_min, convex polyhedron uncertain network multiple time delay control system andIt is at the determinacy case on three summits of convex polyhedron, its maximum time lag border d_maxSimulation result as shown in table 1:

The given d of table 1_minSituation under, calculate d_max

As can be seen from Table 1, the convex polyhedron that has obtaining based on right of freedom matrix method becomes many when probabilisticThe relevant progressive stable condition of lagging network networked control systems time lag and deterministic network networked control systems are on three tops of convex polyhedronThe relevant progressive stable condition of time lag obtaining based on inequality method when point has higher conservative, ensures uncertain network controlThe maximum of system stability processed allows time lag to allow time lag little than the maximum of deterministic network networked control systems.

Step 4, given dynamical system original state is x (0)=[58]^TTime, and MatlabLMI instrument in step 2The result that case solves, simulates the closed network networked control systems condition responsive of Unequal time lag situation with Matlab, if Fig. 2 is to figureShown in 6.

Fig. 2 and Fig. 3 are the shape of convex polyhedron uncertain network multiple time delay control system under difference maximum time lag borderState response curve, can find out in the time that maximum allowable delay bound increases, and the adjusting time of system stability also increases thereupon, visibleFor convex polyhedron uncertain network networked control systems, time-delay the response time of system. Fig. 2 is the maximum of trying to achieveTime lag border is d_maxCondition responsive curve in=9 situation, when time lag meetsTime, system is stillBe progressive stable, shown the validity of this method.

Fig. 4, Fig. 5 and Fig. 6 be deterministic network networked control systems respectively in the time of three summits of convex polyhedron, maximum time lag limitThe d of boundary_maxThe condition responsive curve of=9 o'clock, with convex polyhedron uncertain network networked control systems at maximum time lag border d_max=9 o'clockCondition responsive curve map 2 relatively, can find out in identical time lag situation, convex polyhedron uncertain network networked control systemsSystem stability regulates the time to grow, and this has also illustrated that the uncertainty of system has affected response time and the stability of systemEnergy.

Claims (5)

1. a stability judging method for uncertain network Systems with Multiple Time-Delays, is characterized in that, specifically comprises the following steps:

Step 1, sets up closed network multiple time delay control system model;

Step 2, is mapped to the uncertainty of closed network multiple time delay control system in convex polyhedron parameter space, obtains protrudingPolyhedron uncertain network multiple time delay control system model;

Step 3, structure includes the Lyapunov function of multiple time delay information;

Step 4, utilizes right of freedom matrix method, the convex polyhedron uncertain network multiple time delay control system that determining step 2 obtainsRobust Delay-Dependence Stability, obtain the relevant robust stability adequate condition of time lag; If it is abundant to meet the relevant robust stability of time lagCondition, uncertain network Systems with Multiple Time-Delays is stable, if do not meet, uncertain network Systems with Multiple Time-Delays is unstableFixed.

2. the stability judging method of uncertain network Systems with Multiple Time-Delays as claimed in claim 1, is characterized in that, described inClosed network multiple time delay control system model in step 1 is:

Wherein,

Positive integerFor time become time lag; A_p,B_p,C_pBe the real constant coefficient matrix of suitable dimension, k is current sampling instant,For the system state variables of augmentation, A_c,B_c,C_c,D_cIt is the real constant coefficient matrix of suitable dimension.

3. the stability judging method of uncertain network Systems with Multiple Time-Delays as claimed in claim 2, is characterized in that, described inConvex polyhedron uncertain network multiple time delay control system model in step 2 is:

Wherein, A_0α,A_1α…,A_3αIt is sytem matrix group.

4. the stability judging method of uncertain network Systems with Multiple Time-Delays as claimed in claim 3, is characterized in that, described inIn step 3, the Lyapunov function that includes multiple time delay information of structure is as follows:

V(x(k))＝V₁+V₂+V₃+V₄

Wherein,

V₁＝x^T(k)P_αx(k)

In formula, P_α,R_1α,R_2α,R_3α∈R^n×nFor relying on parameter alpha_i(t) symmetric positive definite matrix, 0≤α_i(t)≤1，i＝1,2,…,N is Bounded Real scalar function.

5. the stability judging method of uncertain network Systems with Multiple Time-Delays as claimed in claim 4, is characterized in that, described inThe adequate condition of the relevant robust stability of time lag of the convex polyhedron uncertain network multiple time delay control system in step 4 is:

For time become time lag There is symmetric positive definite matrix P_α＝P_α ^T＞0，Q_α＝Q_α ^T＞0，And the matrix N of arbitrarily suitable dimension_iα,M_iα,S_iα(i＝1,2)，X_α,Y_α,Z_α>=0 can makeFollowing one group of LMI is set up:

Λ_23α＝d_maxΞ_23α

Λ_24α＝d_maxΞ_24α

Λ_34α＝d_maxΞ_34α

Ξ_ijα＝X_ijα+Y_ijα+Z_ijα，i，j＝1，2，3

。