H_? Control For Linear Unceratin Time Delay System

Time-delay is a common phenomenon in practical engineering,which often leads to oscillation and instability of the system.Time-delay systems are infinite dimensional,and thus it is always difficult to analyze the stability and controller design.so the study of time-delay systems has always been a hot and difficult point in Modern control theory.This paper mainly draws on the classical methods proposed by the predecessors for dealing with the time-delay systems,and combines recent research results to improve and popularize them.It focuses on how to reduce the conservativeness of the conclusions proposed,and deeply analyzes the Stability and Controller Design of Uncertain Linear Systems with Time-Delay.The conributions are summarized as follows:Firstly,A novel method is proposed in this note for stability analysis of systems with a time-varying delay.At the same time,according to the different ways of dealing with the (?)(t),two LMIs forms of time-varying delay nominal system stability conditions are proposed.Then the conclusion is promoted to the time-varing delay norm systems of bounded uncertainties and polynomial type uncertainties.In addition,according to the structure of the constructed functional,The conclusion obtained are extended to the stability conditions with delay-dependent/delay-rate-independent stability and the stability conditions related to delay-independent/delay-rate-dependent.Numerical examples are given to demonst-rate the effectiveness and the merits of the proposed method.Second,the method of processing the quadratic integral term is extended to the time-delay uncertain descriptor system,and the Lyapunov-Krasovskii functional is constructed by combining the system equations.And Calculating the bounded real lemma(BRL)condition.Based on the discussion of the state feedback of the slow subsystem,the systems can ensures the prescribed H_?performance level.Numerical examples are provided and draw its singular value curve to demonstrate the effectiveness of the proposed H_?controlle design methodes.Finally,dealing with the design of robust H_?controller for uncertain linear time-varying delay systems.The influence of the construced Lyapunov-Krasovskii functional and the selection of the inequality on the conservative conclusion is discussed in detail.Then contructing suitable Lyapunov functionals,The bounded real lemma(BRL)conditions are derived,and then discussing the H_?controller design problem.Through the numerical examples and singular value analysis,the proposed methodes are demonstrated.Besides,This paper gives an equivalence proof of the stability conditions of two nominal systems,which is more general than the traditional method and does not depend on specific systems and functionals.In addition,when the BRL condition is extended to the H_?controller design problem,nonlinear items will appear in the matrix inequality,we provide an iterative algorithm using convex optimization as an althernative solution.