Delay System Stability And Robust H_ ¡Þ Filter Design

Time delay phenomenon is often encountered in many practical industry sys-tems.And uncertainties always exist in many practical systems. It is well known that the existence of time delays and uncertainties in a system cause instability or bad system performance. Hence the problem of stability of time delay systems has received considerable attention in the last decades. With the Mordern control the-ories'development,lots of results of linear normal systems have been generalized to nonlinear system one after another. In recent years,design of robust H∞filter has received considerable attention.The purpose is to design a filter assuring asymptoti-cally stability and a prescribed H∞performance level for the filtering error dynamic system,irrespective of the uncertainties and the time delays,which is based on an uncertainty signal. Thereby, according to the results at the present time, this paper investigates the robust stability about uncertain neutral systems with mixed time-varying delays as well as a design of robust H∞filter for uncertain neutral systems with time delays.The main conclusions in this paper are as follows:(1)Stability criteria for uncertain neutral systems with mixed time-varying de-lays.This paper investigates the stability condition for a class of uncertain neutral systems with time-varying delays and nonlinear uncertainties.Choosen the appror-iate Lyapunov function,used the transform of Leibnitz-Newton formula and Linear Matrix Inequality(LMI),a new delay-dependent stability condition of nonlinear neu-tral systems with time-varying delays is derived. Finally,numerical examples show the effectiveness of our results and much less conservative.(2)A design of robust H∞filter for uncertain neutral systems with time de-lays.In this paper,the problem of robust H∞filtering for uncertain neutral systems with time delays is considered.The purpose is to design full filters assuring asymptot-ically stability and a prescribed H∞performance level for the filtering error dynamic system,irrespective of the uncertainties and the time delays.Based on the Lyapunov stability theory,sufficient condition for the existence of full order H∞filters is pro-posed by LMI approach such that the filtering error system is asymptotically sable and satisfies a prescribed attenuation level of noise:(?)O< O, X - Y> O.Moreover,an explicit parametrization of all desired full robust H∞filter is presented when these conditions are feasible. A numerical example is given to demonstrate the feasibility and effectiveness of the design.