Research On Stability For Delayed Systems

In many practical problems,time delay is a common phenomena.It is encountered in various engineering systems,such as distributed networks containing lossless transmission lines,signal processing,static image processing,robot control,nuclear reactors,pattern recognition,microwave oscillators,combinatorial optimization,neural networks,etc.Because time delay can easily cause instability and oscillations in a system,the stability and control of systems with delays has become an important topic of theoretical studies and engineering application.More and more researchers focus on analysis of these systems via different approaches and presented a number of useful and interesting results.In this thesis,the problems of asymptotic stability for many different kinds of delayed systems are investigated and several stability criteria are presented in terms of linear matrix inequality(LMI).Compared with previous literature,these results are more useful and less conservative.In the first chapter,the background of the research into time delay systems and some basic notions are introduced,such as the conception of LMI,LMI Toolbox,S-procedure,etc.In the second chapter,a less conservative delay-range-dependent criterion for systems with interval time-varying delay and nonlinear perturbations is established.Considering the range information of the time-varying delay,a novel Lyapunov-Krasovskii functional is presented.The free-weighting matrices are used.The robust stability of linear neutral systems with time-varying delay and nonlinear perturbations is investigated in the third chapter.Using new Lyapunov-Krasovskii functionals,less conservative delay-dependent sufficient criteria are derived.In the fourth chapter,the stability is considered for linear neutral systems with mixed delays and norm-bounded uncertainty.Both delay-derivative dependent criterion and delay-derivative independent criterion are provided.In the fifth chapter,a less conservative delay-dependent conditions is established for delayed neural networks.Using the delay fractioning approach and considering the integral of the cross product term of the state and nonlinear function not emerged in previous results,a novel Lyapunov-Krasovskii functional is presented.Unlike the existing results,the activation functions considered in this chapter are assumed to be neither monotonic,nor differentiable,nor bounded.In the last chapter,a new Lyapunov-Krasovskii functional is constructed for delayed Hopfield neural networks,and several free-weighting matrices and S-procedure are employed to derive the delay-dependent stability criterion.Numerical examples are given to demonstrate the effectiveness and less conservativeness of those presented criteria in every chapter.At the end of this thesis,the main points are summarized and the future research prospect in the analysis of delayed systems is proposed.