Robust L1 filtering for switched LPV systems with average dwell time

Abstract

In this paper, a robust L1 filtering method is proposed for a class of switched linear parameter varying (LPV) systems in which the state-space matrices and the time delay rely on real-time measured parameter. By using multiple delay-dependent Lyapunov-Krasovskii function, the delay-dependent L1 performance criterion for the switched LPV systems is first established. As there exists coupling between Lyapunov function and system parameter matrices, we utilized a slack matrix variable to decouple it. Because of the dependence on parameter, approximate basis function and gridding technique are utilized, and the solution for the L1 filters can be transformed into finite dimensional convex optimization problem. Based on the switching logic with the minimum average dwell time (ADT) and parameter linear matrix inequalities (PLMIs) technique, the resulting filters guarantee the filtering error systems to be exponentially stable with a prespecified L1 disturbance attenuation level. A numerical example is presented to verify the effectiveness of the proposed method.