Admissibility and controller design for rectangular descriptor time-delay systems☆

This paper studies the analysis and stabilizing control problems of rectangular descriptor time-delay systems (RDTDSs), with system matrix pair (E,A) E R-m"n . Firstly, the results for the uniqueness, impulse-freeness, and stability of the solution of rectangular descriptor systems (RDSs) are given in the case of m < n . Secondly, the delay-dependent and delay-independent results based on linear matrix inequalities (LMIs) for RDTDSs are proposed. Subsequently, for RDTDSs with m >= n , the sufficient condition for impulse-freeness is presented. Additionally, admissibility results for RDTDSs with m > n analogous to the case of m < n are provided. Furthermore, a state feedback controller design method is presented, which ensures the admissibility of the closed-loop system when m >= n . Finally, three examples are provided to demonstrate the validity of the obtained results. (c) 2024 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.