A Generalized ${\mathcal{H}}_{2}$ Filtering of Uncertain Discrete-Time Singular Systems with Time-Varying Delays

Abstract

In this paper, the problem of delay-dependent robust filtering of linear discrete-time singular systems with time-varying delays and polytopic uncertainties is thoroughly investigated. We employ a linear regular filter to ensure its practical implementation. We establish the filter admissibility condition, then using an improved augmented Lyapunov–Krasovskii functional, we develop new delay-dependent filtering design conditions based on generalized \({\mathcal{H}}_{2}\) performance criteria and without relying on overbounding for both the nominal and uncertain cases. Seeking computational convenience, all the developed results are cast in the format of strict linear matrix inequalities (LMIs) and a numerical example is presented.