Stability Analysis And Robust H_? Controller Design For A Class Of Time-varying Delay Systems Based On Delay Decomposition Method

In many practical systems,the problem of time delay often occurs,which is one of the most common problem encountered in many dynamic systems such as mechanical systems,chemical processes and neural network systems.As we all know,the occurrence of time delay may result in system performance degradation,or even destroy the stability of control system.Hence,to analyze the stability of time-delay system and understand the influence of time delay on systems`stability,has became an important research topic.In the past few decades,the stability analysis of time-delay systems has drawn great attention and many valuable research methods and research results have also been obtained.In this paper,we first analyze the stability of a class of time-varying delay systems based on delay decomposition method and design a robust H_?controller.Finally,we analyze the stability of a nonlinear time-varying delay system based on T-S model and design a H_?robust controller.This article mainly studies from the following aspects:(1)Firstly,based on the mathematic model of time-varying time-delay system,by fully utilize time-delays information and its derivative information,an appropriate Lyapunov-Krasovskii functional is constructed based on the delay decomposition method.And put the positive definite judgment on a part of the complete Lyapunov-Krasovskii functional,combining with convex combination principle and Jensen's inequality,the stability of a class of time-varying delay systems is finally analyzed.Considering the uncertainty of the system parameters in the real system,the stability of a class of system with time-varying delay and uncertain parameters is analyzed.Finally,the validity of the used method is verified by numerical examples and system state simulations.(2)Secondly,it is considered that the actual system may be disturbed by the external environment;the performance of a class of linear time-varying delay systems is analyzed.Then,considering the robustness of the system with time-varying delay under external perturbation,the robust controller with time-varying delay is given based on the robust H_?performance controller design.Finally,the validity of the robust controller design is verified by the given examples and simulations.(3)Based on the previous search,we considering the T-S fuzzy model based nonlinear system,the nonlinearity is represented by nearization.Firstly,the H_?performance of T-S fuzzy nonlinear time-varying delay system is analyzed.Secondly,the robust H_?performance of uncertain T-S fuzzy nonlinear systems with time-varying delay is analyzed.Finally,robust H_?controller design for a class of time-varying delay systems based on delay decomposition is presented.In the end,numerical examples and simulations are given to illustrate the effectiveness of the results obtained.