Exponential Stability Of Classes Of Systems With Time-Delay

The existence of time delay in real life usually leads to the control systems becoming instable and having a bad performance. Therefore, in the past few years, the analysis and synthesis of time-delay systems, especially the stability analysis have played a significant role in the international control field. This paper mainly discusses the problems of exponential stability of linear discrete time system with time-delay and neutral-type system with time-delay, and the robust exponential stability of time-delay systems with norm-bounded uncertainties.The main contents are summed up three chapters as follows.In chapter 1, time-delay systems and uncertain systems are introduced. The research status and theoretical basis about the stability subject of time-delay systems are also given. And the main research works are summarized.In chapter 2, the exponential stability problem for a class of linear discrete time systems with time delay is investigated. Firstly, by making up proper Lyapunov-Krasovskii functional and using stability theory and skillful operational technique, a delay-dependent sufficient condition of exponential stability is derived in terms of linear matrix inequalities (LMIs) for the linear discrete-time systems with time delays. Secondly, the result is applied to uncertain discrete systems with time delay and a new criterion of the robust exponential stability is also proposed. Lastly, numerical examples are given to show the effectiveness and feasibility of the obtained result.In chapter 3, the exponential stability problem for a class of neutral systems with time delay is considered. Based on constructing a new type of Lyapunov-Krasovskii functional which contains some triple-integral terms and using free-weighting matrix approach and adding zero term, a delay-dependent sufficient condition of exponential stability is derived for neutral time-delay systems. The result is applied to neutral-type systems with norm bounded parameter uncertainties and time delay. Lastly, numerical examples are given to show the effectiveness and feasibility of the obtained results.