Dimensionality Reduction Filter Design For Uncertain Time-delay Systems

Time-delay is a phenomenon of nature,and it exists widely and connot be avoided.Uncertainty must be appearing in the process of using model dealing with the practical problems.So the filtering problem of uncertain systems with time delay always has been concerned by researchers'.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 the study of filtering problem 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_∞reduced-order filtering problem of uncertain singular systems with multiple time varying state delays and uncertain neutral system,and the design of the L₂-L_∞reduced-order filtering problem of uncertain stochastic system with time delay.Based on a Lyapunov functional method,sufficient conditons for design roduced-order filter are established in terms of linear matrix in inequallity(LMI),and the special forms of filters are given.The main contents in this paper are as follows:(1) The problem of robust H_∞reduced-order filter design for uncertain singular systems with multiple time-varying state delays is considered.The purpose is to design linear filters with a specified order lower than the given system assuring asymptotic stability and a prescribed H_∞performance level for the filtering error dynamic system,irrespective of the uncertainties and the time delays.Sufficient conditions for the solvability of this problem are obtained.Moreover,an explicit parametrization of all desired robust H_∞reduced-order filter is presented when these conditions are feasible.All these results are expressed in term of the original system matrices without decomposition,which makes the design procedure simple and directly.A numerical example is given to demonstrate the feasibility and effectiveness of the conclusion.(2) robust H_∞reduced-order filter of uncertain neutral system with distributed delays is investigated.First,an operator is difined,then a new Lyapunov functional is constructed in terms of the above defined operator.By Lyapunov stability,the sufficient conditions to asymptotic stability with an performanceγof the filter error system are presented.The expected linear filter can be obtained by sloving LMI. The conclusion of filter is not only generalized to uncertain neutral systems,but also using the example to illustrate the conclusion has a better performance.(3) This paper solves the problem of L₂-L_∞reduced-order filter design for uncertain stochastic systems with time-delays.First,given a sufficient condition of filtering error system is asyptotic stability with an L₂-L_∞performanceγ.Then the L₂-L_∞reduced-order filter can be obtained by the sufficient condition,which make the closed-loop system is asyptotic stability with an L₂-L_∞performanceγ, respect to the uncertainty.