Design of Robust L2 - L∞ Filter for Linear Uncertain Time-delay Systems

This paper investigates robust L₂ - L_infin filtering problem for a class of linear uncertain time-delay systems. The uncertainties in the system are time-varying and bounded, and time delays are time-varying. The objective is to design linear memoryless filters such that for all uncertainties, the resulting augmented system is robust stable independent of delays and satisfies the proposed L₂ - L_infin performance. Based on Lyapunov stability theory in time-delay systems, a sufficient condition on the existence of robust L₂ - L_infin filters is derived. The problem of robust L₂ - L_infin filters is turned into the solution problem of linear matrix inequalities. A numerical example is given to demonstrate the effect of the proposed approach