Asynchronous H_∞ filtering fault detection for discrete-time switched linear systems

Abstract

This article studies the asynchronous H ∞ filtering fault detection for discrete-time switched linear systems with mode-dependent average dwell time (MDADT). Firstly, a series of mode-dependent fault detection filters are designed, and augmented with original switched systems to construct a residual evaluation system. However, in practice, the switching of the filter often lags behind the corresponding subsystem. To deal with this, the running time of the subsystem is divided into two parts: the matched and the mismatched. Then the asynchronous switched residual evaluation system is obtained, and global uniform exponential stability (GUES) and exponential H ∞ performance of asynchronous switched system are guaranteed by using μ-dependent discontinuous multi-Lyapunov functions and MDADT method. The sufficient conditions for the existence of designed filter are given in terms of linear matrix inequalities (LMIs), and parameter matrices of the designed filter and MDADT can be obtained by solving these LMIs. Finally, the effectiveness of the proposed method is demonstrated by two examples.