Robust L₂ - L_∞ Filtering for Uncertain Nonlinearly Parameterized Stochastic Systems with Time-Varying Delays

Abstract

This paper is concerned with the problem of robust L₂ - L_∞ filtering for uncertain stochastic time-delay systems in the nonlinear fractional transformation (NFT) form. Attention is focused on the design of both full-order and reduced-order filters, guaranteeing robust stochastic stability and a prescribed level of L₂ - L_∞ performance for the filtering error system. A parameter-dependent Lyapunov functional is employed to solve the problem. The concerned filters are not only parameter dependent but also have the NFT form. Sufficient conditions for the existence of such filters are presented in terms of certain linear matrix inequalities (LMIs). Desired filters are explicitly expressed based on the solutions to the proposed LMIs. A numerical example is provided to demonstrate the effectiveness of the proposed method.