A Joint Design Method of Distributed Gossip Protocol and Controller for Networked Coupled Systems

Abstract

The present invention relates to the field of power system communication optimization control technology, solves the technical problem of nonlinear and non-convex constraints in the control communication probability design process of traditional distributed power systems, and particularly relates to a distributed Gossip protocol and controller joint design method for networked coupling systems, the method comprising the following steps: obtaining system parameters of each sub-region in a controlled multi-region power system, and establishing a continuous-time system state space model of each sub-region based on the system parameters; discretizing the continuous-time system state space model to obtain a discrete-time system parameter matrix, and constructing a distributed controller system model according to the discrete-time system parameter matrix under the Gossip protocol; constructing a nonlinear matrix inequality based on the design target of the distributed controller. The present invention achieves the purpose of improving the robustness and anti-interference performance of large-scale power systems and reducing the computational burden and communication bandwidth.

Description

Technical Field

[0001] The present invention relates to the technical field of power system communication optimization control, and in particular to a distributed Gossip protocol and controller joint design method for a networked coupling system. Background Art

[0002] Many engineering systems can be described by the large-scale system LSS model, such as power systems. Generally speaking, three different control strategies have been studied for large-scale systems LSS, namely centralized control, decentralized control, and distributed control. Distributed control is considered to be a trade-off between centralized control and decentralized control and has been widely studied in the past few years. In the study of distributed control of large-scale systems LSS, it is usually assumed that each sub-controller communicates with all its neighbors at every moment. However, this assumption is not easy to meet in actual engineering when computing and communication resources are limited. Therefore, various communication protocols are used to manage the communication order.

[0003] In the traditional communication protocol Gossip protocol, each sub-controller receives information from only one randomly selected neighbor with equal probability, rather than receiving information from all neighbors at every moment. Therefore, the use of this protocol saves network bandwidth and reduces the transmission of data packets in the communication network. However, it ignores the fact that in practical applications, especially in power systems, the communication probability between subsystems is not equal and consistent, and it will be interfered by various factors such as communication equipment and technology, environmental conditions, etc. Therefore, by designing and optimizing the communication probability, it has a significant impact on improving the system performance of large-scale interconnected systems. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention provides a joint design method of a distributed Gossip protocol and controller for a networked coupled system, which solves the technical problems of nonlinear and non-convex constraints in the control communication probability design process of traditional distributed power systems, thereby achieving the purpose of improving the robustness and anti-interference performance of large-scale power systems and reducing the computational burden and communication bandwidth.

[0005] To solve the above technical problems, the present invention provides the following technical solutions: a method for jointly designing a distributed Gossip protocol and a controller for a networked coupling system, the method comprising the following steps:

[0006] S1. Obtain system parameters of each sub-region in the controlled multi-region power system, and establish a continuous-time system state space model of each sub-region based on the system parameters;

[0007] S2. Discretize the continuous-time system state space model to obtain the discrete-time system parameter matrix , and according to the discrete time system parameter matrix under the Gossip protocol Build a distributed controller system model;

[0008] S3, construct nonlinear matrix inequalities based on the design goals of distributed controllers;

[0009] S4. Decouple the nonlinear matrix inequality through Schur's lemma and inequality scaling to obtain the communication probability containing only the coupling term Matrix inequalities for ;

[0010] S5. Use the GA genetic algorithm and LMI linear matrix inequality solution algorithm to obtain the optimal communication probability ;

[0011] S6. The optimal communication probability Substitute it into the matrix inequality of the distributed control system model to stabilize the multi-regional power system.

[0012] By means of the above technical solution, the present invention provides a method for jointly designing a distributed Gossip protocol and a controller for a networked coupling system, which has at least the following beneficial effects:

[0013] 1. The distributed Gossip protocol and controller joint design method proposed in the present invention are applied to interconnected power systems. Compared with the centralized controller requiring information from all subsystems and the system performance degradation caused by each subcontroller in decentralized control using only local information, the proposed distributed Gossip protocol and controller joint design method can ensure that the interconnected power system reduces the communication bandwidth under the premise of stability.

[0014] 2. The present invention applies the Gossip protocol to the interconnected power system. The information communication in the communication network dispatched by the communication protocol can avoid data conflicts and reduce the communication and computing burden. At the same time, compared with the equal probability communication of the traditional Gossip protocol, the present invention optimizes the communication probability and effectively minimizes the limited time. performance indicators and improve the robustness of the system.

[0015] 3. The present invention optimizes the communication probability under the Gossip protocol The method combines the traditional LMI method with the GA genetic algorithm to solve the optimal communication probability, which can reduce the conservatism in the controller design and effectively improve the system performance; the introduction of the GA genetic algorithm can well handle the non-convex and nonlinear terms in the sufficient conditions for solving the distributed controller, and significantly reduce the finite time performance indicators, thereby improving system performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0017] Figure 1 is a flow chart of the control method of the present invention;

[0018] Figure 2 A schematic diagram of a power system framework of four regions in a multi-region power system of the present invention;

[0019] Figure 3 It is an execution flow chart of the GA genetic algorithm of the present invention;

[0020] Figure 4 It is a fitness function value iteration curve diagram of the genetic algorithm of the present invention;

[0021] Figure 5 It is a state trajectory curve diagram of the four-region power system of the present invention. DETAILED DESCRIPTION

[0022] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific implementation methods, so that the implementation process of how the present application uses technical means to solve technical problems and achieve technical effects can be fully understood and implemented accordingly.

[0023] In recent years, the control problem of large-scale systems (LSS) has attracted extensive research attention. The reason is that many engineering systems can be described by LSS models, such as power systems. LSSs are usually composed of a large number of interconnected subsystems. The dynamics of one subsystem affects the dynamics of other subsystems, which makes the control of LSSs a challenging task. Generally speaking, three different control strategies have been studied for LSSs, namely centralized control, decentralized control, and distributed control. However, centralized control may suffer from heavy communication and computational burdens because the centralized controller requires information from all subsystems. On the other hand, decentralized control may lead to system performance degradation or even destroy system stability because each subcontroller only uses local information. Therefore, distributed control is considered to be a trade-off between centralized control and decentralized control and has been widely studied in the past few years. In this control strategy, local information and information from neighbors are collected to form local control inputs. In the study of distributed control of LSSs, it is usually assumed that each subcontroller communicates with all its neighbors at every moment. However, this assumption is not easy to meet in practical engineering when computing and communication resources are limited. Therefore, various communication protocols are used to manage the communication sequence.

[0024] In the traditional communication protocol Gossip protocol, each sub-controller receives information from only one randomly selected neighbor with equal probability, rather than receiving information from all neighbors at every moment. Therefore, the use of this protocol saves network bandwidth and reduces the transmission of data packets in the communication network. However, it ignores the fact that in practical applications, especially in power systems, the communication probability between subsystems is not equal and consistent. It will be interfered by various factors such as communication equipment and technology, environmental conditions, etc. The design and optimization of communication probability has a significant impact on the improvement of system performance of large-scale interconnected systems. The present invention introduces a genetic algorithm (GA) to The coupling term of is processed, and the conservatism of controller design is effectively reduced by combining GA genetic algorithm with linear matrix inequality LMI, minimizing the finite time performance indicators and improve the robustness of the system.

[0025] In order to solve the technical problems of nonlinear and non-convex constraints in the traditional distributed power system control communication probability design process, please refer to Figure 1-Figure 5 This embodiment proposes a distributed Gossip protocol and controller joint design method for networked coupling systems. This embodiment optimizes the communication probability between subsystems under the Gossip communication protocol. The Genetic Algorithm (GA) is used in combination with the Linear Matrix Inequality (LMI) to design the controller to achieve a strong and fast response control effect on the interconnected power system, while optimizing the minimum finite time of the distributed controller. The method comprises the following steps:

[0026] S1. Obtain the system parameters of each sub-region in the controlled multi-region power system, and establish a continuous-time system state space model for each sub-region based on the system parameters; the system parameters include frequency offset , Interconnection line power deviation , Generator output power deviation , Generator valve position deviation , the damping constant of the generator set , speed reduction coefficient , Generator inertia , frequency deviation constant , turbine time coefficient , Governor time coefficient And the synchronous modulus between the tie lines ,in .

[0027] The continuous-time system state space model for each sub-region is:

[0028] ;

[0029] in,

[0030] ;

[0031] ;

[0032] ;

[0033] in, is the frequency offset; is the tie line power deviation; is the generator output power deviation; is the generator valve position deviation; is the frequency deviation constant; is the damping constant of the generator set; Generator inertia; is the speed reduction coefficient; is the turbine time coefficient; is the governor time coefficient; is the synchronous modulus between the tie lines; for The transpose of for The transpose of , means the neighbor set of the i-th discrete-time system model; is the load disturbance; for The derivative of .

[0034] S2. Discretize the continuous-time system state space model to obtain the discrete-time system parameter matrix , and according to the discrete time system parameter matrix under the Gossip protocol Construct a distributed controller system model; the four-region power system framework diagram selected in this embodiment is as follows Figure 2 As shown in the figure, the system consists of four sub-areas, among which area 1 is interconnected with area 2, area 2 is interconnected with area 1 and area 3, area 3 is interconnected with area 4, and area 4 is interconnected with area 3; in the i-th area, there are several observers to observe the system output of the area, and the collected information is transmitted to the i-th controller of the distributed control layer. The control signal generated by the i-th controller is transmitted to the i-th area as the control output, and the communication network between the controller and the observer is scheduled by the Gossip protocol.

[0035] In step S2, the specific process includes the following steps:

[0036] S21. Discretize the continuous-time system state space model to obtain a discrete-time system model, wherein the discrete-time system model is:

[0037] ;

[0038] in,

[0039] ;

[0040] Where k represents the kth sampling moment of the discrete-time system model; , Represent the state vector, control input and external disturbance of the i-th discrete-time system model respectively; , means the neighbor set of the i-th discrete-time system model; is the delayed term of neighbor j of the ith subsystem Status;

[0041] S22. Obtain discrete time system parameter matrix based on discrete time system model ; According to the discrete time system model, the parameter matrix can be obtained .

[0042] S23. Introducing random variables in the Gossip protocol , and construct an observer-based distributed controller, where , which means that the i-th sub-controller receives the state vector from the j-th sub-controller and state estimation ,in ,Specifically, the distributed controller is:

[0043] ;

[0044] in, , represents the estimated state of the i-th distributed controller; the matrix represents the observer gain; the matrix represents the controller gain; ; , represents the measured output of the i-th distributed controller; are the known matrices of the system equations, derived from , represents the ith subsystem, j represents the neighbor j of the ith subsystem; is the delayed term of neighbor j of the ith subsystem state estimation; is the delayed term of neighbor j of subsystem i The measurement output.

[0045] S24. Establish the probability distribution of communication variables of the distributed controller in the Gossip protocol. In the Gossip protocol, each subsystem can only randomly receive information transmitted by one of its neighbors at a certain time. Therefore, the communication variables must satisfy the following probability distribution:

[0046] ;

[0047] in, is the communication probability; is a random variable The probability distribution of is a random variable, which is different from ; m represents the neighbor of the i-th subsystem, which is different from j.

[0048] S25. Construct a distributed control system model according to the distributed controller. The constructed distributed control system model is:

[0049] ;

[0050] Where k represents the kth sampling moment of the discrete-time system; Represent the state vector, control input, external disturbance, performance output and measurement output of the i-th distributed controller respectively; are all real matrices of appropriate dimension; , which means the neighbor set of the ith subsystem, represent The cardinality of ,and , is a constant.

[0051] S3. Construct nonlinear matrix inequalities based on the design objectives of distributed controllers; the design objective is to make the multi-regional power system meet the requirements of external disturbances. Exponential stability under zero initial conditions and finite time Minimum, design goals are:

[0052] ;

[0053] in, is the interference attenuation level index; N is the number of sub-controllers; k is the sampling time; They represent the state vector, external disturbance and performance output of the i-th distributed controller respectively; E is the mathematical expectation.

[0054] This example uses the Lyapunov equation to prove the stability of the multi-regional power system and the finite time Minimum performance index , the Lyapunov equation is:

[0055] ;

[0056] in, , for The transpose of are all positive definite matrices; t and are the summation variables of the delayed terms, respectively.

[0057] The nonlinear matrix inequality of the controller is:

[0058] ;

[0059] in,

[0060] ;

[0061] ;

[0062] ;

[0063] And must meet ;

[0064] In the above formula, represent The cardinality of is the communication probability; are all real matrices of appropriate dimension; It is the interference attenuation level indicator; All are positive definite unknown matrices; For the Subsystem Neighbor Pair The communication probability of Respectively The control gain and No. Neighbor Pair The control gain of Respectively The observation gain and No. Neighbor Pair The observation gain of For the Subsystem Neighbor Pair The correlation matrix of for Subsystem Neighbor's Correlation matrix; is the unit matrix; are all unknown constants greater than 0.

[0065] S4. Decouple the nonlinear matrix inequality through Schur's lemma and inequality scaling to obtain the communication probability containing only the coupling term Matrix inequality of; except for the communication probability The above matrix inequality also has coupling terms similar to For this nonlinear term, in step S4, specifically:

[0066] Using Schur's lemma to multiply the nonlinear matrix inequality on the left and on the right by its transpose, and then scaling the two inequalities, we can get a new communication-only probability The matrix inequality of the coupling term is:

[0067] Multiply the resulting nonlinear matrix inequality on the left:

[0068] ;

[0069] in, is a diagonal matrix; is the unit matrix; All are positive definite matrices; For subsystem The number of neighbors of Both , represents the basis of the null space; , They represent multiplication by the large matrix. The part of the term and multiplying by the large matrix Part of an item;

[0070] Right multiply it by its transpose:

[0071] ;

[0072] in, is a positive definite matrix; for ;

[0073] Using the two inequalities to scale up and down, we can get a new communication-only probability The matrix inequality of the coupling term is:

[0074] ;

[0075] in,

[0076] ;

[0077] ;

[0078] ;

[0079] ;

[0080] in,

[0081] ;

[0082] ;

[0083] ;

[0084] ;

[0085] ;

[0086] ;

[0087] In the above formula, are all positive definite matrices; are all unknown matrices of appropriate dimensions; They are and The neighbor j of subsystem i Neighbors; is the number of neighbors of neighbor j; is the number of neighbors of subsystem i.

[0088] S5. Use the GA genetic algorithm and LMI linear matrix inequality solution algorithm to obtain the optimal communication probability ; For the coupling term, that is, the communication probability To solve the problem, this embodiment adopts the GA genetic algorithm. Since it is a probability problem, this embodiment controls the initial value between 0 and 1 very well, providing a good population initialization range for the subsequent use of the GA genetic algorithm, making the search space more efficient.

[0089] As a preferred implementation of step S5, the optimal communication probability is obtained by applying a solution algorithm combining a GA genetic algorithm and an LMI linear matrix inequality. , please refer to Figure 3 , in order to optimize the communication probability The execution flow chart of the GA genetic algorithm used. The specific process includes the following steps:

[0090] S51, randomly generate an initial population according to the probability of belonging to the initialization range [0,1];

[0091] S52, due to the equality constraints , introduce dynamic penalty function ,in, , is the number of iterations;

[0092] S53, using the LMI tool to solve the linear matrix inequality group for each individual, if there is a solution, calculate the corresponding fitness function value; if there is no solution, assign a sufficiently large value to the fitness function value of the individual; considering the equality constraints of step S52 and the dynamic penalty function , the fitness function of GA genetic algorithm is expressed as:

[0093] ;

[0094] in,

[0095] ;

[0096] ;

[0097] in, is transposed.

[0098] Since the goal of this embodiment is to minimize the interference attenuation level index In order to keep the solution with large fitness function value, this embodiment selects to meet this requirement.

[0099] S54, perform selection, crossover, mutation, and elite retention GA operations for iteration. If the maximum number of iterations is reached, the optimal individual obtained during the iteration is saved, which is the optimal communication probability. ; Otherwise return to step S53.

[0100] In this embodiment, the Gossip protocol based communication probability optimization in the present invention The distributed controller design method combines the traditional LMI method with the GA genetic algorithm to reduce the conservatism in the controller design process and effectively improve the system performance. The introduction of the GA genetic algorithm can well handle the nonlinear terms in the sufficient conditions for solving the controller and more effectively minimize the interference attenuation level index. , suppress the impact of interference on the system, thereby improving system performance.

[0101] S6. The optimal communication probability Substitute it into the matrix inequality of the distributed control system model to stabilize the multi-regional power system.

[0102] In summary, the GA genetic algorithm is used to assist in optimizing the communication probability. The fitness function value obtained in the design algorithm, the iteration curve is as follows Figure 4As shown in the figure, the red solid line represents the finite time obtained by the equal probability communication between subsystems in the previous Gossip protocol. Performance indicators The red dotted line represents the optimal individual in the GA genetic algorithm iteration process. The blue solid line represents the average fitness value during the iteration of the GA genetic algorithm. The solution value obtained by the method proposed in the present invention is significantly lower than the solution value of the prior art.

[0103] The optimized communication probability Applied to power system, the state curve of the system is as follows Figure 5 As shown. The four sub-graphs in the figure describe the state trajectory diagrams of the four state components of the four sub-areas of the power system, namely area 1, area 2, area 3 and area 4. The states of the four state components are frequency deviation , Interconnection line power deviation , Generator output power deviation , Generator valve position deviation .from Figure 5 It can be seen that each state component of each sub-region can converge, that is, the performance requirement of finite-time stability is achieved within the specified time (30 seconds in this embodiment).

[0104] Those skilled in the art can understand that all or part of the steps in the above-mentioned embodiment method can be completed by instructing the relevant hardware through a program, so the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0105] Each embodiment in this specification is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the above embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiments.

[0106] The above implementation methods have been described in detail. Specific examples are used herein to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

Claims

1. A joint design method of distributed gossip protocol and controller for networked coupled systems, It is characterized in that The method comprises the following steps: S1. Obtain the system parameters of each sub-region in the controlled multi-region power system, and establish a continuous-time system state space model for each sub-region based on the system parameters. The system parameters include frequency offset , Interconnection line power deviation , Generator output power deviation , Generator valve position deviation , the damping constant of the generator set , speed reduction coefficient , Generator inertia , frequency deviation constant , turbine time coefficient , Governor time coefficient And the synchronous modulus between the tie lines ,in ; S2. Discretize the continuous-time system state space model to obtain the discrete-time system parameter matrix , and according to the discrete time system parameter matrix under the Gossip protocol Build a distributed controller system model; S3, construct nonlinear matrix inequalities based on the design goals of distributed controllers; S4. Decouple the nonlinear matrix inequality through Schur's lemma and inequality scaling to obtain the communication probability containing only the coupling term Matrix inequalities for ; S5. Use the GA genetic algorithm and LMI linear matrix inequality solution algorithm to obtain the optimal communication probability The specific process includes the following steps: S51, randomly generate an initial population according to the probability of belonging to the initialization range [0,1]; S52, due to the equality constraints , introduce dynamic penalty function , state penalty function for: ； in, , is the number of iterations; S53, using the LMI tool to solve the linear matrix inequality group for each individual, if there is a solution, calculate the corresponding fitness function value; if there is no solution, assign a sufficiently large value to the fitness function value of the individual. The fitness function of the GA genetic algorithm is expressed as: ； in, ; S54, perform selection, crossover, mutation, and elite retention GA operations for iteration. If the maximum number of iterations is reached, the optimal individual obtained during the iteration is saved, which is the optimal communication probability. ; Otherwise return to step S53; S6. The optimal communication probability Substitute it into the matrix inequality of the distributed control system model to stabilize the multi-regional power system.

2. According to claim 1, the distributed Gossip protocol and controller joint design method, It is characterized in that In step S1, the continuous-time system state space model of each sub-region is: ； in, ； ； ； in, is the frequency offset; is the tie line power deviation; is the generator output power deviation; is the generator valve position deviation; is the frequency deviation constant; is the damping constant of the generator set; Generator inertia; is the speed reduction coefficient; is the turbine time coefficient; is the governor time coefficient; is the synchronous modulus between the tie lines; for The transpose of , means the neighbor set of the i-th discrete-time system model; is the load disturbance; for The derivative of .

3. According to claim 1, the distributed Gossip protocol and controller joint design method, It is characterized in that In step S2, the specific process includes the following steps: S21. Discretize the continuous-time system state space model to obtain a discrete-time system model, wherein the discrete-time system model is: ； in, ； Where k represents the kth sampling moment of the discrete-time system model; , Represent the state vector, control input and external disturbance of the i-th discrete-time system model respectively; , means the neighbor set of the i-th discrete-time system model; is the delayed term of neighbor j of the ith subsystem Status; S22. Obtain discrete time system parameter matrix based on discrete time system model ; S23. Introducing random variables in the Gossip protocol , and construct an observer-based distributed controller, the distributed controller is: ； in, , represents the estimated state of the i-th distributed controller; the matrix represents the observer gain; the matrix represents the controller gain; ; , represents the measured output of the i-th distributed controller; are the known matrices of the system equations, derived from , represents the ith subsystem, j represents the neighbor j of the ith subsystem; is the delayed term of neighbor j of the ith subsystem state estimation; is the delayed term of neighbor j of subsystem i The measurement output of S24. Establish the probability distribution of communication variables of distributed controllers in the Gossip protocol. The probability distribution is: ； in, is the communication probability; is a random variable The probability distribution of is a random variable, which is different from ; m represents the neighbor of the ith subsystem, which is different from j; S25. Construct a distributed control system model according to the distributed controller. The constructed distributed control system model is: ； Where k represents the kth sampling moment of the discrete-time system; Represent the state vector, control input, external disturbance, performance output and measurement output of the i-th distributed controller respectively; are all real matrices of appropriate dimension; , which means the neighbor set of the ith subsystem, represent The cardinality of ,and , Is a constant.

4. The distributed Gossip protocol and controller joint design method according to claim 1, It is characterized in that In step S3, the design goal is to make the multi-regional power system meet the external disturbance Exponential stability under zero initial conditions and finite time Minimum, design goals are: ； in, is the interference attenuation level index; N is the number of sub-controllers; k is the sampling time; They represent the state vector, external disturbance and performance output of the i-th distributed controller respectively; E is the mathematical expectation.

5. The distributed Gossip protocol and controller joint design method according to claim 1, It is characterized in that In step S3, the nonlinear matrix inequality of the distributed controller is: ； in, ； ； ； And must meet ; In the above formula, is the number of neighbors of neighbor j; is the number of neighbors of subsystem i; is the communication probability; are all real matrices of appropriate dimension; It is the interference attenuation level indicator; All are positive definite unknown matrices; For the Subsystem Neighbor Pair The communication probability of Respectively The control gain and No. Neighbor Pair The control gain of Respectively The observation gain and No. Neighbor Pair The observation gain of For the Subsystem Neighbor Pair The correlation matrix of for Subsystem Neighbor's Correlation matrix; is the unit matrix; are all unknown constants greater than 0.

6. The distributed Gossip protocol and controller joint design method according to claim 1, It is characterized in that In step S4, specifically: Using Schur's lemma to multiply the nonlinear matrix inequality on the left and on the right by its transpose, and then scaling the two inequalities, we can get a new communication-only probability The matrix inequality of the coupling term is: Multiply the resulting nonlinear matrix inequality on the left: ； in, is a diagonal matrix; is the unit matrix; All are positive definite matrices; For subsystem The number of neighbors of Both , represents the basis of the null space; , They represent multiplication by the large matrix. The part of the term and multiplying by the large matrix Part of an item; Right multiply by its transpose: ； in, is a positive definite matrix; for ; Using the two inequalities to scale up and down, we can get a new communication-only probability The matrix inequality of the coupling term is: ； in, ； ； ； ； in, ； ； ； ； ； ； In the above formula, are all positive definite matrices; are all unknown matrices of appropriate dimensions; They are and The neighbor j of subsystem i Neighbors; is the number of neighbors of neighbor j; is the number of neighbors of subsystem i.

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