Admissibility and state feedback control for discrete-time rectangular descriptor systems

作者：Wentao Geng, Chong Lin · 发表于：International Journal of Systems Science · 年份：2024 · DOI：10.1080/00207721.2024.2434888 · 被引用次数：2 · 研究领域：Stability and Control of Uncertain Systems、Adaptive Control of Nonlinear Systems、Control and Stability of Dynamical Systems

This paper studies the admissibility and state feedback stabilising control problems of discrete-time rectangular descriptor systems (DRDSs) with system matrix pair (E,A)∈Rm×n. We first present definitions and lemmas for the consistency of initial condition, generalised regularity and causality of DRDSs. Secondly, we establish the equivalence relations between the admissibility of RDSs and their corresponding square systems. Then we give the admissibility results of DRDSs in the case of m≥n and m<n, respectively, which are necessary and sufficient. With these conditions, we present the sufficient condition for a state feedback stabilising controller to make the closed-loop system admissible. Finally, three examples are given to show the effectiveness of our methods.