Study On Stability And Stabilization Of Several Time - Delay Systems

Delay often occurs in a variety of systems. The research for time-delay systems has important theoretical and applied value. In this thesis, several classes of switched systems with time delay and neutral delay systems are studied, and some innovations in the theory are obtained.Firstly, the problem of robust stabilization for a class of switched nonlinear systems with time-varying delays is studied. Using the method of average dwell time, by constructing Lyapunov-Krasovskii functional and using the linear matrix inequality technique, a new criterion for the exponential stabilization of a class of switched systems with time-delay is established. Then we give new sufficient conditions for the exponential stability of a class of time-delay linear systems. Based on the results obtained, a new criterion of robust exponential stabilization for uncertain switched nonlinear systems with time-delay is established. We give sufficient conditions of the robust exponential stabilization for a class of uncertain switched linear systems with time-delay. Finally, a numerical example is given to illustrate the effectiveness of the results.Secondly, the robust stability of neutral systems with mixed time-varying delays and nonlinear perturbations is studied. By constructing the new Lyapunov-Krasovskii functional and using the free weight matrix method and the linear matrix inequality technique, novel sufficient conditions of exponential stability for a class of neutral nonlinear systems with mixed time-varying delays is established. Then the delay dependent robust stability criteria for neutral systems with mixed time-varying delays and nonlinear perturbations are given. In this paper, a new criterion of asymptotic stability for a class of uncertain linear neutral systems and a new criterion of asymptotic stability for a class of neutral nonlinear systems with constant delays are given. Finally, two numerical examples are presented to verify the validity of the results.Finally, the output feedback stabilization problem for a class of positive switched linear systems with multiple time varying delays is studied. By con-structing appropriate copositive Lyapunov-Krasovskii functional and using the free weighting matrix technique, a lemma for a time delay positive system is giv-en. Then, based on this lemma, a new criterion of exponential stability for time delay positive switched systems with time delays is established by means of the average dwell time method. The output feedback controller is designed, and a new criterion of output feedback stabilization for positive switched linear systems with multiple time varying delays is presented. For the positive switched systems with multiple constant time delays, we also establish a new criterion of exponential stability.