Robust H_∞ Control For Systems With Time-delays

Delay is usually presented to lots of pragmatic systems, it is a physicalphenomenon that existed widely in nature, furthermore, delay is the root induced insta-bility, so the research of robust stability analysis and controller's designing for delayedsystems is important. In recent years, singular system and neutral system are focusedon widely by many researchers because they are playing an important role in practicalcontrol problems gradually, lots of results of linear normal system have been general-ized to singular system and neutral system one after the other. Whereas, their complexmechanism make it difficult to research robust stability analysis and robust H_∞control.Particularly, the study of robust stability analysis and robust H_∞control for singularsystem and neutral system with time-delays are on junior moment. Thereby, accordingto the complexion at the present time, this paper investigates the problems of robust H_∞control for uncertain singular system with multiple time-delays, uncertain singular systemwith time-varying delay, uncertain neutral system with time-varying delay and uncertainneutral type descriptor system with mixed time-delays. Based on a Lyapunov functionalmethod, sufficient conditions for designing H_∞state-feedback controllers are establishedin terms of linear matrix inequality(LMI). The main conclusions in this paper are:(1) According to the results of linear and singular systems with time-delay, H_∞control problem of uncertain singular system with multiple time-delays is considered usingthe method dealing with normal systems containing time-delay. A sufficient condition forthe existence of a memoryless H_∞state-feedback controller is obtained based on thedesigning method of LMI, a numerical example is also given to illustrate the applicabilityof the proposed approaches that extended by linear and singular systems with time-delay.(2) Some results of non-fragile control are generalized to H_∞theory of singularsystem ulteriorly in this paper. Considering objective uncertain and the controller's un-certain synchronously, non-fragile robust H_∞control is described for uncertain singularsystem with time-varying delay. By taking a proper Lyapunov-Krasovskii functional,delay-dependent conditions for the existence of non-fragile robust H_∞controllers are pre-sented in terms of LMI. Numerical examples are given to illustrate the validity of ourmethod.(3) The problem of delay-dependent and delay-independent robust H_∞control is introduced for uncertain neutral systems with time-varying delays. Based on a Lyapunov-Krasovskii functional method, delay-dependent and delay-independent bounded real lemma(BRL) for time-varying delay uncertain neutral systems is established in terms of a linearmatrix inequality. Using the obtained BRL, a delay-dependent and delay-independentsufficient condition for the existence of a state feedback controller, which ensures asymp-totic stability and a prescribed H_∞performance level of the closed-loop system for alladmissible uncertainties, is proposed.(4) Robust H_∞control is presented for a class of uncertain neutral type descrip-tor systems with mixed time-delays. The class describes linear state models with norm-bounded uncertain system parameters and unknown constant mixed delays. A sufficientcondition for designing a memoryless state-feedback controller is established by the stabil-ity of the operator D(t)=Ex(t)-Gx(t-h) brought forward by Hong Li. All the resultsis given by LMI, it is convenient to solve.