Meta-sequence-dependent H∞ filtering for switched linear systems under persistent dwell-time constraint

Abstract

Abstract This paper is concerned with H ∞ filtering problem for a class of discrete-time switched linear systems under persistent dwell-time (PDT) constraint. A concept of meta sequence list consisting of finite switching subsequences is presented, which can represent all admissible PDT switching sequences by concatenating the list elements. Two novel Lyapunov functions only based on the meta sequence list are constructed, which break the limitation of traditional mode dependency and quasi-time dependency. Two equivalent stability criteria are accordingly developed, and the widely-used nonconvex stability conditions for PDT switched linear systems are proved to be sufficient to them. Moreover, the presented convex stability criterion is further extended to l 2 -gain computation and H ∞ filter design. The designed meta-sequence-dependent (MSD) filter can guarantee that the filtering error system is globally uniformly asymptotically stable with a standard H ∞ performance index, which contrasts with the indices in weighted or parameter-dependent forms, i.e., weaker noise attenuation, in the existing literatures of switched systems under average dwell-time or PDT constraints. Two examples are provided to illustrate the effectiveness of the developed results.