Stability Analysis And Synthesis Of Linear Systems With Time-varying Delays

During the last several decades, the time-delay phenomena are often encountered in various practical systems, such as engineering systems, biologies systems, economics systems, neural networks systems, and so on. Therefore, the study of time-delay systems have been reported and various approaches have been proposed in the literature and the references therein. On the other hand, since time-delays are the main cause of oscillation, divergence or instability, considerable efforts have been made in the analysis and synthesis of dynamical systems.This paper considers the interval time delay system and time delay systems with uncertain. By using Lyapunov second method and linear matrix inequalities(LMI) the-ory, the stability criteria and controller-designing has been obtained on linear time delay system. The main results contain the robust stability of linear time delay system with uncertain, the stability of linear system with interval time delay and the robust H∞controller-designing method of time delay system with uncertain.The first chapter introduces the research meaning, the significance and the current research results of the linear systems with time-varying delay, as well as the main work of this paper. The second chapter proposes some based concepts, theories and lemmas to get the main results. The third chapter obtains the stability criteria for linear time-delay system in the first by using the combination of optimize delay piecewise and Jensen inequality methods. Furthermore, the stability criteria for linear time-delay system with uncertain has been obtained by using the same method. The forth chapter obtains the stability criteria for linear system with interval time-delay in the first by using the combination of the free-weighting matrix and Jensen inequality methods. Hereafter, the stability criteria for linear time-delay system with delay lower limit is zero has been obtained by using the same method. The fifth chapter obtains the H∞stability criteria for uncertain time-delay system with external disturbance by using the combination of delay piecewise and relative convex methods. In addition, the controller has been designed for the system with input.In the end, this paper summarizes the work which has been done, and put forward the suggestion for the future work.