Research On Stability For Some Time-delay Neural Networks And Consensus For Multi-agent Systems

Neural networks are considered to be one of the simplified mathematical models.In the implementation of neural networks,time delay is unavoidable due to the limited switching speed of the amplifier.The existence of time delay will inevitably destroy the stability and performance of the system.Stability is one of the most basic dynamic characteristics of delayed neural networks.In many engineering practices,it is not enough to know only that the system converges to the equilibrium point,but also that it is necessary to know the convergence rate of the system trajectory towards the equilibrium point.Exponential stability can provide faster convergence speed than asymptotic stability,so it has attracted wide attention.In addition,dissipativity is closely related to system stability,and it can reveal more system performance,such as passivity,H? control,and so on.Therefore,this thesis studies the exponential stability problem and passivity analysis of delayed neural networks,respectively,and the dissipativity of memristor-based neural networks,and draws less conservative stability criteria.On the other hand,multi-agent systems consist of a series of interoperable agents and can perform tasks that a single agent can not perform.When information is exchanged between adjacent agents on the communication network,due to the influence of the limited network bandwidth,communication delay is inevitable in the transmission process,and its existence will destroy the consensus of the multi-agent systems.In addition,in many practical problems,the state information of all agents can not be obtained completely,but for linear multi-agent systems,control protocols based on the output information of adjacent agents are designed to achieve the consensus of multi-agent systems.Because of the limited network bandwidth and unreliable communication channel,it is difficult to transmit continuous signals in the process of signal transmission.In order to reduce the number of updates of the controller and the number of communications between agents and reduce energy consumption,sampling control is usually used when designing conformance protocols or algorithms.Therefore,we design a control protocol based on output information of adjacent agents with communication delay and a control protocol with sampling information,respectively,and investigate the consensus problem of linear multi-agent systems.This main works of this thesis are:1.The exponential stability problem of neural networks with interval time-varying delay is studied.Firstly,we propose the extended free-matrix-based double integral inequality,which is compared with free-matrix-based double integral inequality.By comparison,it is found that the latter is a special case of the former.Next,in the case of the same Lyapunov-Krasovskii functional,the extended free-matrix-based double integral inequality and Wirtinger-based double integral inequality are used to estimate the double integral terms in the derivative of Lyapunov-Krasovskii functional,respectively,and some delay-dependent exponential stability criteria are given for delayed neural networks.2.The passivity problem of uncertain neural networks with interval time-varying delay is studied.Firstly,an augmented Lyapunov-Krasovskii functional containing two triple integral terms is constructed,and an auxiliary function-based integral inequality is used to manipulate the augmented single integral terms in the derivative of Lyapunov-Krasovskii functional.Secondly,a special form of the auxiliary function-based integral inequality is applied to deal with the delay-product-type term,which derives from the triple integral term.In addition,In the case of the same Lyapunov-Krasovskii functional,some delay-dependent passivity criteria for normal delayed neural networks are obtained by omitting delay-product-type term at this time.These methods are extended to investigate passivity problem of delayed neural networks with parameter uncertainties.3.In order to solve the problem of dissipativity for memrisor-based neural networks with time-varying delay,this thesis firstly applies differential inclusions and set-valued maps to convert delayed memristor-based neural networks into the conventional delayed neural networks.Then,we construct Lyapunov-Krasovskii functional with a time-delay coefficient quadratic term of the state vector and a triple integral term,and use the reciprocal convex technique and Wirtinger-based integral inequality to estimate the derivative of Lyapunov-Krasovskii functional,delay-dependent criteria in terms of linear matrix inequalities are obtained to ensure that neural networks are strictly dissipative.Moreover,the proposed method is extended to investigate the passivity analysis of the considered systems.4.The thesis is concerned with the consensus problem for linear multi-agent systems with communication delays.Firstly,a consensus protocol is built upon the relative output information between adjacent agents in the presence of time-varying delays.When the feedback gain matrix K is known,by using the Lyapunov theory and the convex combination technique,some sufficient conditions are obtained in the form of linear matrix inequalities(LMIs)for consensus of linear multi-agent systems.When K is unknown,variable substitution method is introduced to transform the non-linear matrix inequalities into linear matrix inequalities.5.To solve the consensus problem of linear multi-agent systems,a consensus control protocol based on sampling information is designed.Firstly,using state transformation,the consensus problem of linear multi-agent systems is equivalently converted into the stability problem of linear time-delay systems.Next,by employing Lyapunov theory and a delay processing method,delay-dependent stability criteria are derived via 2(n-1)linear matrix inequalities.Finally,according to convex combination technique,2(n-1)linear matrix inequalities can be equivalently transformed into four ones.