Stability And Synchronization Of Several Classes Of Time-delay Systems

In practical engineering applications,such as network systems,power systems,nuclear reactors,chemical engineering systems,and neural networks,there exist phenomenons of time delay widely.Although the delay is very small,it often affects the dynamic performance of the system,and has an impact on the stability of the system.Ignoring the phenomenon of time delay can lead to design defects and incorrect conclusions.Therefore,the influence of time delay on the dynamics system is an important factor that must be considered in many practical engineering problems.In recent years,it has received a great deal of attention.This thesis is based on the Lyapunov stability theory,using the Lyapunov-Krasovskii function method,free weighting matrix technique,linear matrix inequality,neural activation controller and LMI technology,analyzes and studies the problem of synchronization and stability of switched neural network with time-varying delays,switched neural networks with time-varying delay and s fuzzy mixed-delay systems.Some new criteria and new discoveries have been obtained.In this thesis,we solve the global exponential delay synchronization problem of switched neural networks with time-varying delay and general activation.Finally,to illustrate the effectiveness,we present a numerical example.Complete theoretical results will be used in future practice,such as image encryption.This paper investigated the problem of global exponential anti-synchronization of switched neural networks with time-varying delays and lag signals via the neural activation controllers,which is applied to secure communication and image encryption.A numerical example is used to prove the validity of the results.By employing a novel Lyapunov functional method,an LMI-based delay-dependent H? analysis scheme is proposed by an improved free-weighting matrix approach,which takes the relationship among the time delays,their lower and upper bounds into account to obtain some less conservative delay-dependent H? analysis criteria without ignoring any useful terms in the derivative of the Lyapunov functional.Finally,a numerical example has been carried to show the effectiveness and merits of the proposed method.