A L₂-L_∞ Filter Design For Stochastic Time-Delay Systems

This paper focuses on the problem of L₂-L_∞ filtering design for stochastic time-delay system. By using free weighting matrix, oIt ? ’s differential formula and Lyapunov function. The L₂-L_∞ filtering design method of this kind of system is obtained in the form of linear matrix inequalities.First, we review the origin and general situation of control theory, and introduce the linear control theory, the background and research results of stochastic system.In the second place, for the delay-dependent L₂-L_∞ filtering design for stochastic time-delay systems, by choosing appropriate Lyapunov functional and introducing the method of free weighting matrix, the sufficient conditions for the design of this kind of filtering are obtained based on the solution of linear matrix inequality—ensure that the filtering error system is asymptotically stable and satisfies the L₂-L_∞ performance, at last, a numerical example proves the value of propose method is effective.Third, on the basis of the last chapter, the same Lyapunov functional is used to study the delay-dependent with output L₂-L_∞ filtering design for stochastic time-delay systems and a numerical examples prove the value of propose method is effective.Finally, we summarized the article, and pointed out the research direction in the future.