The H_? Control For One-Sided Lipschitz Nonlinear System With Time-Varying Delay

The one-sided Lipschitz system,as a broader form of expression than the Lipschitz system,has attracted widespread attentions in recent years.This paper mainly studies the problem ofH_?control for one-sided Lipschitz nonlinear time-delay systems.As far as the author knows,there are many observer designs for one-sided Lipschitz nonlinear systems.However,on the basis of time delay,less research has done on theH_?control for one-sided Lipschitz nonlinear system.This motivates our research on theH_?control for one-sided Lipschitz nonlinear time-delay systems.This article is mainly divided into the following sections for description.First,the basic theories used in this paper are introduced,which mainly includes the theory of Lyapunov stability analysis,linear matrix inequality,and the introduction of subsequent related lemmas.Then the model of the flexible link manipulator is introduced,based on the Lyapunov stability analysis theory,combined with the one-sided Lipschitz condition,a more basic Lyapunov function has been selected to discuss the stability of the flexible link manipulator system.The observer for the system is designed to obtain sufficient conditions for the asymptotic stability of the observation error system,which lays the foundation for subsequent observer-based controller design.Secondly,through the research experience in linear time-delay systems,a Lyapunov function that can reflect the time-delay information and a controller determined by the original state and the time-delay state are introduced to design a stabilized controller for the one-sided Lipschitz system with time-varying delay.The improved Wirtinger inequality,Schur complement lemma,one-sided Lipschitz condition,and quadratic internal bounded condition are used to deal with the system time delay,sufficient condition for system stabilization is derived,and the controller and observer gain expressions are given.At last,the flexible link robotic arm model was selected for simulation to prove the correctness of the proposed theory,at the same time,numerical example of unstable system is used to prove the superiority of the Lyapunov function selected in this paper.Finally,considering the problems of disturbance and uncertainty in the actual system,the robust stabilization analysis and disturbance suppression of the one-sided Lipschitz time-delay system are studied.At first,we consider the case where the disturbance is zero,and obtain the sufficient condition for the asymptotic stability of the one-sided Lipschitz time-delay system with uncertainty,as well as the controller gain and observer gain.Then consider the condition where the disturbance is not zero,and design the disturbance suppression controller to obtain the sufficient condition for the system to meet theH_?performance index in the form of a linear matrix inequality.The numerical example 1 of the flexible link manipulator and numerical example 2prove the correctness of the proposed theory.