Reliable H ∞ Filtering for Discrete-Time Switched Singular Systems with Time-Varying Delay

Abstract

This paper is concerned with the reliable H ∞ filtering problem against sensor failures for a class of discrete-time switched singular systems with time-varying delay. A practical sensor failure model, which consists of a scaling factor with upper and lower bounds to the output measuring is considered. The purpose is to design a switched full-order H ∞ filter such that, for all possible sensor failures, the resulting filtering error system is regular, causal, and uniformly asymptotically stable with a guaranteed H ∞ performance index under arbitrary switching signals. By using the switched Lyapunov function approach and establishing a finite sum equality, a delay-dependent bounded real lemma (BRL) for the filtering error systems is derived via linear matrix inequality (LMI) formulation. An improved BRL is also established by introducing additional slack matrix variables to realize the decoupling between the filtering error system matrices and the Lyapunov matrices. Then, based on the decoupled BRL, the existence criterion of the desired filter is obtained by employing the LMI technique. Some numerical examples are provided to illustrate the effectiveness and the potential of the proposed methods.