CN106877398A - Micro battery decentralized coordinated control method based on multiple agent - Google Patents

Abstract

A kind of micro battery decentralized coordinated control method based on multiple agent, its content includes：Build two-layer multiple agent Coordinated Control Scheme；The internal structure of two-layer multiple agent is designed, lower unit intelligent body is designed as including conversion zone and consults the hybrid agent of layer；Upper strata intelligent body is designed as including study and evaluation module, database, knowledge base, Two-stage control module and action executing module；Micro battery decentralised control scheme is proposed, the decentralised control of distributed power source is double-closed-loop control, designs Fractional Order PID Controller；The parameter optimization of Fractional Order PID Controller of being adjusted with particle swarm optimization algorithm；Distributed and coordinated control device is designed based on uniformity control theory；The validity of the program is verified with l-G simulation test.The present invention provides not only economically feasible but also a safely and reliably control strategy for the distributed power source of micro-capacitance sensor, it is ensured that micro-capacitance sensor being capable of safe and stable operation under island mode.

Description

Micro battery decentralized coordinated control method based on multiple agent

Technical field

The invention belongs to intelligent grid control field, and in particular to a kind of micro battery decentralized coordinating control based on multiple agent Method processed.

Background technology

In recent years, distributed generation technology had obtained the concern of domestic and foreign scholars, and was widely used in power system.Point Cloth power supply is including photovoltaic power generation apparatus, wind-driven generator, fuel cell and miniature gas turbine etc..Distributed power generation has to be thrown Money is small, environmentally friendly good and the advantages of flexibility high, but also there are problems that simultaneously it is a lot, such as distributed power source unit access into Originally higher, control relative difficulty etc..Additionally, distributed power source is for bulk power grid, it is a uncontrollable power supply, bulk power grid Have to take the mode of such as limitation, isolation to process distributed power source, to reduce impact of the distributed power source to bulk power grid. Networking of the IEEE1547 standards to distributed power source is dictated：When electric power system fault, distributed power source must be moved back at once Go out operation.This standard greatly limit giving full play to for distributed power source, and the profit of new energy is also limited indirectly With.In order to coordinate the contradiction between bulk power grid and distributed power source, it is that micro-capacitance sensor and user bring to make full use of distributed power source Value and benefit, the concept of micro-capacitance sensor is suggested.Micro-capacitance sensor is by distributed power source, energy storage device, energy converter, phase The small-sized electric system that pass load, monitoring and protection device are collected, can uninterruptedly provide high-quality to critical load Electric energy, it is single controllable relative to outside bulk power grid.Micro-capacitance sensor has grid-connected and two kinds of operational modes of isolated island, positive reason With bulk power grid networking operation under condition, as the supplement of power network；Can not meet locally when electric network fault or the quality of power supply is detected During load power reguirements, micro-capacitance sensor is rapid and bulk power grid disconnects islet operation.No matter micro-capacitance sensor is in grid-connect mode or isolated island Pattern, is required for being effectively controlled the distributed power source in micro-capacitance sensor, therefore to the control of distributed power source in micro-capacitance sensor Technology processed is most important.

Micro-capacitance sensor maintains the stabilization of power network by micro battery, and each micro battery is by controlling flexible power electronics Interface inverter is connected to micro-capacitance sensor, therefore, the design to micro-capacitance sensor lower floor decentralized controller is realized by inverter control. Control problem currently for distributed power source in micro-capacitance sensor generally uses following two control strategies：(1) master-slave control strategy. The control strategy needs for the relevant information of distributed power source to focus on control centre, right after analytical calculation by master controller Each inverter issues control information, but it needs communication line transmission information, therefore has dependence higher to communication, and for Baroque system, it is difficult to realize satisfied control effect.(2) decentralised control strategy.Each distributed power source is according to oneself Local relevant information is independently controlled, it is not necessary to which communicate link, and realizes the plug and play of distributed power source, but with The continuous infiltration of generation of electricity by new energy, the structure of micro-capacitance sensor becomes increasingly complex, decentralised control due to lacking the cooperation between unit, When micro-capacitance sensor is subjected to serious disturbance, the frequency quality of system possibly cannot ensure.Just because of above-mentioned reason, the present invention is proposed It is a kind of to balance two kinds of control methods of control strategy advantage and disadvantage-micro battery decentralized coordinated control side based on multiple agent (MAS) Method.

The content of the invention

Instant invention overcomes deficiency of the prior art, a kind of micro battery decentralized coordinating control based on many intellectual technologies is proposed Method processed.The invention is based on two-layer multi-agent Technology platform, designs not only reasonable effective but also economically viable decentralized coordinated control Strategy so that micro-capacitance sensor being capable of the good control performance of maintenance system under large disturbances.

In order to solve above-mentioned technical problem, the present invention is achieved by the following technical solutions：

A kind of micro battery decentralized coordinated control method based on multiple agent, the method content comprises the following steps：

(1) two-layer multiple agent Coordinated Control Scheme is built, each intelligent body unit of lower floor is local according to oneself Relevant information, carry out independent control；Each intelligent body of lower floor can realize the decentralised control of distributed power source；Coordinate on upper strata Control intelligent body, the operation conditions of information and micro-capacitance sensor according to lower floor's intelligent body is provided to lower unit intelligent body in time Corresponding control mode, it is ensured that micro-capacitance sensor stable operation, realizes that upper strata intelligent body realizes distributed power source based on communication network Coordinate control；

(2) internal structure of two-layer multiple agent is designed, lower unit intelligent body is designed as including conversion zone and consults layer Hybrid agent；Upper strata intelligent body be designed as including study and evaluation module, database, knowledge base, Two-stage control module and Action executing module；

(3) micro battery decentralised control scheme is proposed, the decentralised control of distributed power source is double-closed-loop control, including based on inverse Become the open sea wharf of device droop characteristic and based on the control of improved PID voltage x currents inner ring, design Fractional Order PID control Device；

(4) parameter optimization of Fractional Order PID Controller of being adjusted with particle swarm optimization algorithm；

The optimization method of pid parameter has a lot, such as gradient method, simplex method, genetic algorithm, although these methods all have There is good optimizing characteristic, but there are some drawbacks.Gradient method requirement object function can continuously lead；Simplex method receives initial value Influence with material calculation is larger, it is easy to converge on locally optimal solution, causes optimizing to fail；Genetic algorithm need replicated, Intersect and mutation operation, evolutionary rate is slow, is also easy to produce Premature Convergence, and its performance has larger dependence to parameter.Particle Group's algorithm (PSO algorithms) has the advantages that parallel processing, strong robustness and adjustable parameter are few, can be found with larger probability and asked The globally optimal solution of topic, and computational efficiency is high, the parameter of Fractional Order PID therefore present invention particle swarm optimization algorithm is adjusted.

(5) distributed and coordinated control device is designed based on uniformity control theory, it is ensured that the one of distributed power source voltage shows And good power-sharing effect, and can effectively suppress the circulation problem between distributed power source；Design multiple agent one Cause property algorithm, each distributed power source only need oneself information and relative intelligent body information, make the defeated of micro battery Go out voltage consistent, the power-sharing effect that can effectively suppress between circulation, and micro battery is more preferable；

(6) validity of the program is verified with l-G simulation test.

Due to using above-mentioned technical proposal, a kind of micro battery decentralized coordinated control based on multiple agent that the present invention is provided Method, compared with prior art with such beneficial effect：

The present invention balances the dispersion of micro-capacitance sensor and concentrates two kinds of advantage and disadvantage of control method, realizes between micro battery Power-sharing, and the dynamic property and robustness of micro battery output voltage and electric current be improved.

The present invention provides not only economically feasible but also a safely and reliably control strategy for the distributed power source of micro-capacitance sensor, Ensure that micro-capacitance sensor being capable of safe and stable operation under island mode.

Brief description of the drawings

Fig. 1 is the micro-capacitance sensor two-layer control structure figure based on multiple agent；

Fig. 2 is the micro battery decentralised control block diagram based on double-closed-loop control；

Fig. 3 is the power controller block diagram of micro battery；

Fig. 4 is the voltage x current controller control principle drawing of micro battery；

Fig. 5 is micro battery parallel model.

Specific embodiment

The present invention is described in further detail with specific embodiment below in conjunction with the accompanying drawings：

A kind of micro battery decentralized coordinated control method based on multiple agent of the invention, the method content includes following step Suddenly：

1st, in micro-capacitance sensor, each micro battery connects a corresponding unit intelligent body, and each intelligent body being capable of root According to the relevant information of oneself part, independent control is carried out, it is not necessary to which communicate link, realize inserting i.e. for distributed power source With.But single intelligent body may be imperfect due to the information grasped, it is impossible to a certain task of complete independently, it is therefore desirable to each intelligence Interaction between body.When external disturbance than it is larger when, only rely on the control between intelligent body unit, micro-capacitance sensor voltage may be caused It is unstable.Therefore two-layer multiple agent Coordinated Control Scheme is built, Fig. 1 show the micro-capacitance sensor two based on multiple agent Layer control structure figure, each intelligent body unit of lower floor carries out independent control according to the relevant information of oneself part；Lower floor each Intelligent body can realize the decentralised control of distributed power source；Control intelligent body is coordinated on upper strata, information according to lower floor's intelligent body with And the operation conditions of micro-capacitance sensor, provide corresponding control mode to lower unit intelligent body in time, it is ensured that micro-capacitance sensor stable operation； Realize that upper strata intelligent body realizes the coordination control of distributed power source based on communication network.

2nd, the internal structure of two-layer multiple agent is designed, lower unit intelligent body is designed as including conversion zone and consults layer Hybrid agent；Upper strata intelligent body is designed as including study and evaluation module, database, knowledge base, Two-stage control module and dynamic Make performing module；

Lower floor decentralised control Agent includes：The element Agent such as DG Agent, load Agent, be broadly divided into conversion zone and Consult layer.Wherein conversion zone includes perceiving, recognizes and action performing module that the characteristic with " perceive and take action " can be perceived External environment condition obtains data and information, while external environment condition can also be acted on.It is by database, study and assessment mould to consult layer Block, local policy module composition, the attribute with " conviction, hope and intention ".The two-layer multi-agent system that the present invention builds, For " principal and subordinate " interbehavior, i.e. higher level please to the coordination control that subordinate's intelligent body sends between subordinate's intelligent body and higher level's intelligent body Ask, with highest priority.And need to interact between each intelligent body unit, mutually coordinated and cooperation, in ability and resource Between support mutually, finally realize the target of system.The method of the two-layer multi-agent Technology for therefore building can ensure that micro-capacitance sensor Safe and stable operation.

3rd, the decentralised control of distributed power source is double-closed-loop control, including the exterior ring power control based on inverter droop characteristic Make and based on the control of improved PID voltage x currents inner ring, design Fractional Order PID Controller；Fig. 2 is shown based on double-closed-loop control Micro battery decentralised control block diagram；Build the power controller of micro battery and the voltage x current controller of micro battery；

Inverter output current and load point voltage are obtained by measurement module, the instantaneous work(of distributed power source output is calculated Rate.Micro-capacitance sensor is may result according to instantaneous power to impact the quality of power supply when being interfered, by low in design Pass filter device obtains mean power, and the mean power that will be obtained compares with reference power, through sagging in power controller Control obtains the amplitude and phase angle of inner ring voltage controller reference voltage, and Fig. 3 show the power controller block diagram of micro battery.

Droop control method is exactly frequency and the end of synchronous generator in the output simulated high-pressure power system for make inverter Droop characteristic between voltage and the active power for being exported and reactive power, and the system output impedance of low pressure micro-capacitance sensor is usual For resistive, the output impedance of inverter can be made in perception by global design, it is ensured that droop characteristic is set up：

F=f_n-m(P-P_n) (2)

V=v_n-n(Q-Q_n) (3)

Wherein, v_od,v_oq,i_od,i_oqIt is d axles and q axle components that inverter output voltage and electric current are changed through Park, f_n,v_n It is reference voltage and frequency, P_n,Q_nIt is specified active and reactive power, m, n are sagging coefficients.

The parameter for using LC wave filters, LC wave filters for the output of inverter is met with lower inequality

10f_n＜ f_c＜ f_s/10 (4)

Wherein,f_cIt is the resonant frequency of LC wave filters, f_nIt is micro-capacitance sensor frequency, f_sIt is to carry Wave frequency rate,.

It is illustrated in figure 4 the voltage x current controller block diagram of micro battery；Voltage x current double -loop control scheme is inverse high-performance One of developing direction of variable power source, ring controller in present invention voltage x current of the design based on Fractional Order PID.Fractional Order PID is The popularization of conventional integer rank PID controller and development, compared to traditional PID controller, many adjustable parameter products of Fractional Order PID Sublevel time λ and differential order μ.The introducing of the two parameters causes that Fractional Order PID Controller has more flexible structure and stronger Robustness, have obvious advantage than traditional PID controller, more preferable control effect can be obtained.

Voltage ring controller uses Fractional Order PID, module to be output as electric current loop reference current, then through electric current loop fractional order Adjustable sinusoidal modulation signal is obtained after PID controller, then as SPWM modulation modules are input to, so as to control inversion The output voltage of device.

The design Fractional Order PID Controller, including following content：

Micro battery voltage x current controller control principle drawing as shown in Figure 4 is obtained, the corresponding governing equation of voltage controller It is as follows：

Wherein, λ, μ are the integration and differential order of voltage controller, K_PV,K_IV,K_DVRatio, integration for voltage controller And differential coefficient, χ_d,χ_q,ASS_d,ASS_qIt is auxiliary variable, F is the feed-forward coefficients of voltage controller, C_fIt is filter capacitor, ω is With reference to angular frequency.

The corresponding governing equation of current controller is as follows：

Wherein, α, β are the integration and differential order of current controller, K_PC,K_IC,K_DCRatio, integration for current controller And differential coefficient, ψ_d,ψ_qIt is auxiliary variable, L_fIt is filter inductance.

The parameter optimization of Fractional Order PID Controller of the 4th, being adjusted with particle swarm optimization algorithm；

The parameter optimisation procedure of the Fractional Order PID Controller includes following content：

(1) initialization constants parameter

Determine population, the dimension of search space, the span of parameter, set maximum iteration, Studying factors with And inertia weight coefficient；

(2) particle is initialized

Initialize speed and the position of particle；

(3) object function is determined

In order to obtain good dynamic characteristic, and larger control input is avoided, the present invention uses following optimal index

Wherein, e (t) is absolute error, and u (t) is the output of controller, t_uIt is rise time, ρ₁,ρ₂,ρ₃It is weight system Number；

(4) adaptive value of each particle is calculated, the adaptive value according to particle updates global and individual extreme value；

(5) speed according to following two formulas more new particle and position；

X_i(t+1)=X_i(t)+V_i(t) (12)

Wherein, ω is inertia weight, c₁And c₂It is Studying factors, is nonnegative constant, φ₁And φ₂It is 2 between [0,1] Individual independent random number；

(6) iterations or required precision are reached, is then terminated, otherwise continue iterative search optimal value.

5th, distributed and coordinated control device is designed based on uniformity control theory, it is ensured that distributed power source voltage consistent and Good power-sharing effect, and can effectively suppress the circulation problem between distributed power source；Design multiple agent is consistent Property algorithm, each distributed power source only need oneself information and relative intelligent body information, make the output of micro battery Voltage is consistent, and the power-sharing effect that can effectively suppress between circulation, and micro battery is more preferable；

Fig. 5 show micro battery parallel model, and Fig. 5 constructs i-th distributed power source two distribution connected in parallel The circuit structure of power supply, can be obtained by Kirchoff s voltage current law,

Micro battery parallel model according to Fig. 5, following state-space model is obtained by Kirchoff s voltage current law,

Wherein, x (t)=[i_ti u_i i_R i_im i_tm u_m i_in i_tn u_n]^TIt is state variable, u (t)=[u_ti u_tm u_tn]^T It is input variable, y (t)=[u_i u_m u_n]^TIt is the output of system；

Consistency protocol is：

WhereinIt is perunit value；

For whole closed-loop systemWherein

Design of feedback is controlledSubstitute the above to：

Then the state space of (14) can be written as：

Wherein,ForThe perunit value of x (t)；

System (14) keeps closed-loop system (17) asymptotically stability under feedback controller, and and if only if has the symmetrical square of positive definite Battle array P₁=P₁ ^T≥0,Meet following condition：

Wherein, Q=Q^T＞ 0, Table Show the maximum singular value of matrix,The minimum non-zero singular value of representing matrix；

If feedback gain matrix

OrderKnowable to (19)

The Riccati equation of formula (18) can be written as

Wherein,Then Q ' may be expressed as：

The liapunov function of selecting system is V (x)=x^TPx；

Suitable c and H is obtained by formula (19) and (20), it is ensured that designed controller can make system stabilization.

6th, the validity of the program is verified with l-G simulation test.

The present invention devises two kinds of checking events：(1) micro battery islet operation, in the load that 0.5s increases by 50%, makes 3 Distributed power source is powered for load jointly, and adds consistency algorithm in 0.5s；(2) 0.5s reduces load, and adds one Cause property algorithm.In both cases, the decentralized coordinated control scheme based on multiple agent using present invention design, energy are proved Ensure that micro battery voltage is consistent, realize power-sharing, and can effectively suppress the circulation between micro battery.

As it will be easily appreciated by one skilled in the art that the foregoing is only preferred embodiment of the present invention, it is not used to The limitation present invention, every any modification, equivalent and improvement made within the spirit and principles in the present invention etc., all should wrap It is contained within protection scope of the present invention.

Claims (3)

1. a kind of micro battery decentralized coordinated control method based on multiple agent, it is characterised in that：The method content includes as follows Step：

(1) two-layer multiple agent Coordinated Control Scheme, phase of each the intelligent body unit of lower floor according to oneself part are built Pass information, carries out independent control；Each intelligent body of lower floor can realize the decentralised control of distributed power source；Coordinate control in upper strata Intelligent body, according to the information of lower floor's intelligent body, and micro-capacitance sensor operation conditions, provide corresponding to lower unit intelligent body in time Control mode, it is ensured that micro-capacitance sensor stable operation, realize that upper strata intelligent body realizes the coordination of distributed power source based on communication network Control；

(2) internal structure of two-layer multiple agent is designed, lower unit intelligent body is designed as including conversion zone and consults the mixed of layer Close intelligent body；Upper strata intelligent body is designed as including study and evaluation module, database, knowledge base, Two-stage control module and action Performing module；

(3) micro battery decentralised control scheme is proposed, the decentralised control of micro battery is double-closed-loop control, including sagging based on inverter The open sea wharf of characteristic and based on improved PID voltage x currents inner ring control, design Fractional Order PID Controller；

(4) parameter optimization of Fractional Order PID Controller of being adjusted with particle swarm optimization algorithm；

(5) based on uniformity control theory design distributed and coordinated control device, it is ensured that distributed power source voltage it is consistent and good Good power-sharing effect, and can effectively suppress the circulation problem between distributed power source；Design is based on multiple agent one Cause property algorithm, each distributed power source only need oneself information and relative intelligent body information, make the defeated of micro battery Go out voltage consistent, the power-sharing effect that can effectively suppress between circulation, and micro battery is more preferable；

(6) validity of the program is verified with l-G simulation test.

2. a kind of micro battery decentralized coordinated control method based on multiple agent according to belonging to claim 1, it is characterised in that： The design Fractional Order PID Controller, including following content：

Obtained by micro battery voltage x current controller control principle, the corresponding governing equation of voltage controller is as follows：

$\left\{\begin{array}{c}{\mathrm{\χ}}_d=(K_{PV}+K_{IV}{S}^{-\mathrm{\λ}}+K_{DV}{S}^{\mathrm{\μ}})(V_{od}^{*}-V_{od})\\ {\mathrm{\χ}}_q=(K_{PV}+K_{IV}{S}^{-\mathrm{\λ}}+K_{DV}{S}^{\mathrm{\μ}})(V_{oq}^{*}-V_{oq})\end{array}\right.---\left(1\right)$

$\left\{\begin{array}{c}{\mathrm{ASS}}_d={\mathrm{Fi}}_{od}-{\mathrm{\ωC}}_f{V}_{oq}\\ {\mathrm{ASS}}_q={\mathrm{Fi}}_{oq}+{\mathrm{\ωC}}_f{V}_{od}\end{array}\right.---\left(2\right)$

$\left\{\begin{array}{c}{i}_{ld}^{*}={\mathrm{\χ}}_d+{\mathrm{ASS}}_d\\ i_{lq}^{*}={\mathrm{\ψ}}_q+{\mathrm{ASS}}_q\end{array}\right.---\left(3\right)$

Wherein, λ, μ are the integration and differential order of voltage controller, K_PV,K_IV,K_DVFor voltage controller ratio, integration and it is micro- Divide coefficient, χ_d,χ_q,ASS_d,ASS_qIt is auxiliary variable, F is the feed-forward coefficients of voltage controller, C_fIt is filter capacitor, ω is reference Angular frequency；

The corresponding governing equation of current controller is as follows：

$\left\{\begin{array}{c}{\mathrm{\ψ}}_{od}=(K_{PC}+K_{IC}{S}^{-\mathrm{\α}}+K_{DC}{S}^{\mathrm{\β}})(i_{ld}^{*}-i_{ld})\\ {\mathrm{\ψ}}_{oq}=(K_{PC}+K_{IC}{S}^{-\mathrm{\α}}+K_{DC}{S}^{\mathrm{\β}})(i_{ld}^{*}-i_{ld})\end{array}\right.---\left(4\right)$

$\left\{\begin{array}{c}{V}_{ld}^{*}={\mathrm{\ψ}}_{od}-{\mathrm{\ωL}}_f{i}_{lq}\\ V_{lq}^{*}={\mathrm{\ψ}}_{oq}+{\mathrm{\ωL}}_f{i}_{ld}\end{array}\right.---\left(5\right)$

Wherein, α, β are the integration and differential order of current controller, K_PC,K_IC,K_DCFor current controller ratio, integration and it is micro- Divide coefficient, ψ_d,ψ_qIt is auxiliary variable, L_fIt is filter inductance.

3. a kind of micro battery decentralized coordinated control method based on multiple agent according to belonging to claim 1, it is characterised in that： The design distributed and coordinated control device, including following content：

According to micro battery parallel model, following state-space model is obtained by Kirchoff s voltage current law：

$\left\{\begin{array}{c}\stackrel{\·}{x}\left(t\right)=Ax\left(t\right)+Bu\left(t\right)\\ y\left(t\right)=Cx\left(t\right)\end{array}\right.---\left(6\right)$

Wherein, x (t)=[i_ti u_i i_R i_im i_tm u_m i_in i_tn u_n]^TIt is state variable, input variable is u (t)=[u_ti u_tm u_tn]^T, y (t)=[u_i u_m u_n]^TIt is the output of system；

Consistency protocol is：

${\hat{e}}_i=\underset{j=m,n}{\Σ}{a}_{ij}({\hat{u}}_i-{\hat{u}}_j)---\left(7\right)$

WhereinIt is perunit value；

ThereforeWherein

Design of feedback is controlled, and is substituted the above to：

$\hat{u}\left(t\right)=-c(L\⊗H)\hat{y}---\left(8\right)$

Then the state space of (6) can be written as：

$\stackrel{\·}{\hat{x}}\left(t\right)=(I_N\⊗A-cL\⊗BCH)\hat{x}\left(t\right)---\left(9\right)$

Wherein,ForThe perunit value of x (t)；

System (6) keeps closed-loop system (9) asymptotically stability under feedback controller, and and if only if has positive definite symmetric matricesMeet following condition：

$\left\{\begin{array}{c}{p}_1={\mathrm{cR}}_{1}L\\ A^T{P}_2+P_{2}A+Q-P_2{\mathrm{BCR}}_2^{-1}{C}^T{B}^T{P}_2=0\end{array}\right.---\left(10\right)$

$c>\frac{{\mathrm{\σ}}_{max}(R_{1}L\⊗(Q-H^T{R}_{2}H))}{{\mathrm{\σ}}_{>0\min }(L^T{R}_{1}L\⊗H^T{R}_{2}H)}>0---\left(11\right)$

Wherein, Q=Q^T＞ 0,Represent square The maximum singular value of battle array,The minimum non-zero singular value of representing matrix；

If feedback control gain is：

$H=R_2^{-1}{C}^T{B}^T{P}_2---\left(12\right)$

OrderKnowable to (11)

$c^2{\mathrm{\σ}}_{>0min}(L^T{R}_{1}L\⊗H^T{R}_{2}H)-{\mathrm{c\σ}}_{max}(R_{1}L\⊗(Q-H^T{R}_{2}H))>0\⇒Q^{\′}\≥0$

The Riccati equation of formula (10) can be written as:

${(I_n\⊗A)}^{T}P+P(I_n\⊗A)+Q-P(I_n\⊗BC)R^{-1}{(I_n\⊗BC)}^{T}P=0$

Wherein,Then Q ' may be expressed as：

$\begin{array}{c}{Q}^{\′}=c^2(L^T{R}_{1}L\⊗H^T{R}_{2}H)-c(R_{1}L\⊗(A^T{P}_2+P_{2}A\left)\right)\\ =c^2(L^T{R}_{1}L\⊗H^T{R}_{2}H)+{\mathrm{cR}}_{1}L\⊗(Q-P_2{\mathrm{BCR}}_2^{-1}{C}^T{B}^T{P}_2)\\ =P_1{R}_1^{-1}{P}_1\⊗P_2{\mathrm{BCR}}_2^{-1}{C}^T{B}^T{P}_2\⊗(Q-P_2{\mathrm{BCR}}_2^{-1}{C}^T{B}^T{P}_2)\end{array}$

The liapunov function of selecting system is V (x)=x^TPx；

$\begin{array}{c}\stackrel{\&CenterDot;}{V}\left(x\right)=2x^{T}P\stackrel{\&CenterDot;}{x}=x^{T}P(I_N\&CircleTimes;A-cL\&CircleTimes;BCH)x\\ =2x^T(P_1\&CircleTimes;P_2)(I_n\&CircleTimes;A)x-2{\mathrm{cx}}^T(P_1\&CircleTimes;P_2)(L\&CircleTimes;BCH)x\\ =x^T(P_1\&CircleTimes;(A^T{P}_2+P_{2}A)-2(P_1{R}_1^{-1}{P}_1\&CircleTimes;P_2{\mathrm{BCR}}_2^{-1}{C}^T{B}^T{P}_2\left)\right)x\\ =x^T(P_1\&CircleTimes;(A^T{P}_2+P_{2}A)-2(P\left(I_n\&CircleTimes;BC\right)\&CircleTimes;R^{-1}{(I_n\&CircleTimes;BC)}^{T}P\left)\right)x\\ =x^T(P_1\&CircleTimes;(A^T{P}_2+P_{2}A)-2(Q+P_1\&CircleTimes;(A^T{P}_2+P_{2}A)\left)\right)x\\ =-x^T(Q^{\&prime;}+c^2{\left(L\&CircleTimes;H\right)}^T(R_1\&CircleTimes;R_2)\left(L\&CircleTimes;H\right))x\&le;-x^T{Q}^{\&prime;}x<0\end{array}$

Suitable c and H is obtained by formula (11) and formula (12), it is ensured that designed controller can make system stabilization.