Separation Principle For Quasi-One-Sided Lipschitz Nonlinear Systems With Time-Delay

In recent decades,the stabilization of nonlinear time-delay systems has been an important research topic of scholars at home and abroad.This is because nonlinear and time-delay are essential phenomena of many practical systems,such as mechanical systems,chemical processes,power systems and aircraft control systems.In many control problems,the availability of the system state is often required.However,as a practical issue,it is not always possible to measure all the system state variables directly.In this case,it is usually necessary to construct a state observer,and then use the reconstructed state to replace the real state for state feedback.Until now,most of the researches on the stabilization of nonlinear systems focus on the nonlinear terms of the system satisfying the classical Lipschitz condition,few results have been on the study of nonlinear time-delay systems with quasi-one-sided Lipschitz condition.Based on this,this paper studies the output stabilization of the nonlinear time-delay systems by utilizing the Lyapunov-krasovskii theory and the quasi-one-sided Lipschitz condition.This paper is divided into the following five parts:In the first part:an introduction of background of topic selection and current conditions of researchIn the second part:the problem of output stabilization for a class of nonlinear time-delay systems is investigated.Firstly,a state observer is designed to estimate the state of the nonlinear delay system by using the quasi-one-sided Lipschitz condition,and it is proved that the quasi-one-sided Lipschitz condition is less conservative than the one-sided Lipschitz condition.Then,a feedback controller is designed to stabilize the nonlinear time-delay system.Furthermore,it is proved that for the observer-based controller,the separation principle holds.That is to say,under the quasi-one-sided Lipschitz condition,the state observer and the feedback controller can be designed separately even though the parameter(A,C)of nonlinear time-delay systems is not detectable and parameter(A,B)is not stabilizable.Finally,a numerical example is provided to verify the efficiency of the main results in this chapter.In the third part,the problem of output stabilization for a class of nonlinear time-delay systems based on the reduced-order observer is studied.Firstly,the sufficient conditions for the existence of reduced-order observer for a class of quasi-one-sided Lipschitz nonlinear time-delay systems are given.Then,based on the reduced-order observer and the feedback controller designed in Chapter 2,we prove that the separation principle holds.That is to say,for a class of nonlinear time-delay systems,the reduced-order observer and the feedback controller can be designed separately.Finally,an example is given to show the effectiveness and feasibility of the results obtained in this chapter.In the fourth part:the problem of output stabilization of nonlinear time-delay systems is extended to discrete-time systems.Firstly,a state observer is designed to estimate the state of discrete-time nonlinear time-delay systems by introducing the quadratic inner-boundness condition and combining with the quasi-one-sided Lipschitz condition.Then,a state feedback controller is designed to stabilize the system by introducing the weak quadratic innerboundness condition and the weak quasi-one-sided Lipschitz condition.Furthermore,the separation principle of discrete-time quasi-one-sided Lipschitz nonlinear time-delay systems is given.In the sense of discrete-time,the state observer and the feedback controller can be also designed separately even though the parameter(A,C)of systems is not detectable and parameter(A,B)is not stabilizable.In the fifth part:summarize the research results of this paper and make a prospect for the further research work.