A Novel Method for Stability and Stabilization of Interconnected Descriptor Systems

Abstract

This paper addresses the issues of stability and stabilization in interconnected descriptor systems. The existing results based on different structures of the Lyapunov equation are not directly applicable to resolving time-varying problems. In this paper, based on the original literature, the stability of the system is re-described and extended, and new results are obtained, these results are extended to encompass time-varying singular systems exhibiting state-space symmetry, which is achieved by introducing a novel Lyapunov functional. The approach in this paper is grounded in the theory of trace inequalities for matrices, establishing a new sufficient condition for the admissibility of interconnected descriptor systems. In the last, an illustrative example demonstrates the feasibility of employing state feedback to render interconnected descriptor systems admissible, affirming the validity of our proposed method.