A new generalized bounded real lemma for continuous-time descriptor systems

Abstract

This paper proposes a new generalized Lyapunov theorem and a new generalized bounded real lemma for continuous-time linear descriptor systems. First, we provide a necessary and sufficient condition in terms of strict linear matrix inequalities (LMIs) for the admissibility of descriptor systems. Subsequently, we demonstrate that a descriptor system is L-2-gain stable if and only if two strict LMIs are feasible. Other than existing results, only one matrix variable in the LMIs needs to be solved that can be indefinite. Some illustrative examples are provided to validate the theoretical results.