H_? Analysis For Systems With Uncertain Additive Additive Time-varying Delays

As is known to us,time-delay occurs in many practical engineering systems widely,and it is a major cause of instability,oscillation,and poor performance.In the past few decades,the stability of delay systems has attracted many scholars' attention.Without loss of generality,by taking two additive delays for example,At first,a more common LKF is constructed based on the delay-partitioning methods to make fully use of the information of the given system to research the result of stability of the systems.Based on the stability criterion and the H_?performance analysis.the H_?control problem will be investigated.We can extend our results to the systems with multiple additive time-varying delays and uncertainties.This thesis is divided into five chapters:In chapter 1,we introduce the background of the research for delay systems,and make a detailed review.On this basis,we indicate the main issues in this paper.In chapter 2,we briefly introduce the theoretical knowledge of stability,such as Jensen's inequality and Lyapunov stability theory,the convex combination lemma and schur complement lemma,which make full preparation for the follow-up work.In chapter 3,the H_?control is revisited for the systems with multiple additive time-varying delays.At first,a more common Lyapunov-Krasovskii functional is constructed based on the delay-partitioning methods to make fully use of the information of the given system.A new stability criterion for the systems with multiple additive time-varying delays is introduced based on the delay-partitioning methods.The reciprocally convex lemma[31]is applied to deal with the derivative of the proposed Lyapunov-Krasovskii functional,Then,based on the stability criterion and the H_?performance analysis.the H_?control problem will be investigated,which is to design a state feedback controller u(t)=kx(t)for the given system such that the closed-loop system is asymptotically stable with the H_?disturbance attenuation lever g.In order to deal with the nonlinear matrix inequalities in the H_?control,the cone complement linearization algorithm is applied,which is helpful to reduce the conservatism of the result.Finally,numerical examples will be demonstrated to illustrate the effectiveness of the proposed method.The result is better than some results have obtained at present already in conservatism.In chapter 4,based on the results of the chapter 3 and the more common Lyapunov-Krasovskii functional which is constructed in chapter 3,we further research the systems with multiple additive time-varying delays and derive a new delay-dependent stability criterion.Finally,numerical examples will be demonstrated to illustrate the effectiveness of theproposed method.In chapter 5,We summarize the result of chapter 3 and chapter 4,and point out the future researching direction.