A new bounded real lemma for discrete‐time linear descriptor systems

This paper presents a new bounded real lemma for discrete‐time linear descriptor systems. We first present a necessary and sufficient condition for the admissibility of discrete‐time descriptor systems expressed in terms of strict linear matrix inequalities (LMIs). We then prove that a discrete‐time descriptor system is ‐stable if and only if a symmetric matrix satisfying two strict LMIs can be found. Two illustrative examples are provided for verification.