Robust H_ ¡Þ Control For Uncertain Time-delay Systems And Guaranteed Cost Control

Time-delay is a physial phenomenon that exists widely in nature,it is usually prensented to lots of practical systems.While in the establishment of mathematical models and the actual objects,there will be the inevitable errors and uncertainties. Time-delay and uncertainty make the system performance and stability decline,so the research of robust stability analysis and controller's designing for delayed systems are important all the time.In recent years,singular system and neutral system are widely focused by many researchers because they are playing an important role in practical control problems gradually.Lots of results of linear normal systems have been generalized to singular system and neutral system one after another. Whereas,their complex mechanism make it difficult to research robust H_∞control and guaranteed cost control.Particularly,the study of robust H_∞control and guaranteed cost control for singular system and neutral system are on junior moment. Thereby,according to the complexion at the present time,this paper investigates the robust H_∞control and guaranteed cost control of uncertain singular systems with time-delay and uncertain neutral systems.The main conclusions in this paper are as follows:(1) The robust H_∞control problem of a class of uncertain singular system with matched and unmatched uncertainties and time-delay is studied.Firstly,the condition of quadratic stabilization is given and the H_∞controller of the systems is analyzed and designed for all admissible uncertainties.Secondly,the corresponding robust H_∞controller is given in terms of the feasible solutions of the LMIs.Finally, the numerical example demenstrates that the robust H_∞controller make the system satisfy quadratic stabilization and H_∞performance index.(2) The non-fragile robust H_∞control problem for a class of uncertain neutral system with time-varying delays is considered.Considering the uncertainties exist both in the systematic matrix and the controller gain,by choosing a Lyapunov functional,some delay-dependent and delay-independent sufficient conditions of the existence of the robust H_∞controller are given by using LMIs.Under the robust H_∞controller's function,the closed-loop system is stable for all admissible uncertainties and closed-loop performance index has a minimal upper bound.Finally, numerical examples are presented to illustrate the feasibility and the effectiveness of the conclusion.(3) The idea of non-fragile guaranteed cost controller is introduced to a class of uncertain singular system with time-delay.Considering the uncertainties exist both in the systematic matrix and the controller gain,based on LMI techniques, the problem of guaranteed cost control is studied.Under the additive perturbation of the controller,the sufficient condition of non-fragile guaranteed cost is presented, and the corresponding controller design is given in terms of the feasible solutions of LMIs.A numerical example is given to illustrate the feasibility of the designed method.(4) The non-fragile guaranteed cost control problem for nonliear uncertain neutral systems is investigated.Firstly,constructing Lyapunov functional,then using Schur completment andφ-procedure lemma,problem is sovled by LMI techniques. Some sufficient conditions for the existence of non-fragile guaranteed cost controller are given and the feedback cotroller is obtained based on the solutions of LMIs. Finally,the numerical example is presented to illustrate the effectiveness of the conclusion.