Robust H_∞ And L₂-L_∞ Filtering For Systems With Time-varying Delay And Uncertainty

The state filtering has been attracting much attention as one of important fields in control theory and engineering application.However,in many practical applications,the statistical properties of exogenous noise signals are rarely known and there are perturbations in system model,so there has been rapidly growing interests in robust filtering.At the beginning of this paper,the author gives the research background of this topic,and then reviews the development situation and research status of the filtering theory, H∞filtering,the robust filtering and the time-delay systems'stability,at the same time,make a summary for the using mathematical tools and the research methods. Secondly, the H∞filtering ,the L₂ - L∞filtering,uncertainty and linear matrix inequality involved are stated.Then this paper mainly discuss the problems of delay-dependent robust H∞and L₂ - L∞filtering for uncertain linear system with time-varying delay.Two cases of time-varying delays are fully considered;One is the time-varying delay being continuous uniformly bounded while the other is the time-varying delay being differentiable uniformly bounded with delay-derivative bounded by a constant.The purpose is to design a filter which make the filtering error system asymptotically stable for all allowable uncertainties and with a prescribed level of H∞and L₂ - L∞noise attenuation.Based on a new integral inequality,delay-dependent sufficient conditions for the existence of such a filter are established in terms of linear matrix inequalities.This method does not require model transformation to reduce conservative.Finally,some examples are given to illustrate the effectiveness of the proposed methodology.At the end of this paper,the author gives some views about the existing problems in robust filtering study.