Stability Study Of Time-delay Sampling Systems

In recent years,with the continuous development and integration of computer network technology and control theory,especially the widespread application of network control systems,the sampled-data delay systems have attracted extensive attention.In practical engineering,stability is the precondition for the system to work normally.On the other hand,due to the change of external environment or modeling errors,the actual system must have uncertainty.Therefore,the study of robust stability of uncertain sampled-data delay systems has important theoretical value and practical significance.In this paper,the stability analysis and state feedback stabilization for sampled-data delay systems are studied.First of all,aiming at the conservatism of standard Lyapunov-Krasovskii functional method and the lack of theoretical basis of non-standard Lyapunov-Krasovskii functional method,a new stability theorem for sampled-data delay systems is established.Based on this theorem,a looped Lyapunov-Krasovskii functional(LLKF)method is proposed.Secondly,for certain sampled-data delay systems,by constructing LLKF and using advanced inequality to estimate its derivative,less conservative stability results are obtained;the stability results are further applied to the uncertain sampled-data delay systems with convex polygon parameter,and the robust stability criterion is derived.Thirdly,based on the stability analysis,the problem of state feedback stabilization of sampled-data delay systems is studied by using LMI method,and the state feedback stabilization controller is designed.Finally,the simulation results show that the controller obtained has the better control effect.The main contents of this paper are as follows:In the first chapter,the background,status and significance of the research on sampled-data delay systems and feedback control are introduced,and the main problems to be studied in this paper are pointed out.In the second chapter,some basic theoretical knowledge and important lemmas needed in this paper are listed to provide theoretical basis and tools for the following stability study for sampled-data delay systems.In chapter 3,the asymptotic stability analysis for sampled-data delay systems is studied.In view of the conservatism of the current standard Lyapunov-Krasovskii functional method,a new asymptotic stability theorem for sampled-data delay systems is established,and a looped Lyapunov-Krasovskii functional method is presented.Constructing a new LLKF by introducing the integral of state on the delay interval[t-d,t]and integrals of the state and the delayed state on the subintervals[t _k,t)and[t,t_k(10)1)of the sampling interval[t _k,t_k(10)1)and using inequalities more advanced than Jensen's inequality and Wirtinger-based inequality to calculate the upper bound of the derivative of LLKF,less conservative stability results are derived.Then,appropriate changes are made to the stability results to accommodate the uncertain situation,and the new robust asymptotic stability results for convex polygon uncertain sampled-data delay systems are derived.Finally,the numerical simulation shows that the results are less conservative than the current ones.In chapter 4,the design of state feedback stabilizing controller for sampled-data delay systems is studied.Based on the stability analysis in the third chapter,the theorem of state feedback stabilizing design for sampled-data delay systems is constructed by transforming the stability results obtained by properly handling the nonlinear term of the control gain K.The controller design problem is converted into the solution to the feasibility problem of LMI,and the controller design methods and steps are given.Finally,a simulation example is given to verify the superiority of the designed controller.The chapter 5 is the summary of the research content and the assumption of the future research work.