H<sub><i>∞</i></sub> filtering of discrete‐time switched singular systems with time‐varying delays
Mohammed Charqi, Noreddine Chaibi, El Houssaine Tissir
Abstract
Summary In this article, the analysis and design problems of H ∞ filtering for a class of discrete‐time switched singular systems with time‐varying delay under an arbitrary switching signal are investigated. The main attention is focused on the design of a linear mode‐dependent filter guaranteeing the regularity, causality, and asymptotic stability of the resulting filtering error system with a prescribed H ∞ performance bound. By using a multiple Lyapunov‐Krasovskii functional, and utilizing the linearization technique, novel sufficient conditions for the solvability of H ∞ problem are derived in terms of linear matrix inequalities. Solving that, the desired filter gains can be determined. Any model transformation of system, which often leads the large computational burden is involved. The free weighting matrix technique is introduced to provide additional degree of freedom, which improves the conservativeness of the developed method. Finally, numerical examples are given to demonstrate the effectiveness and the merit of the proposed approach and to compare the obtained results with some previous works in the literature.