Robust stabilization for uncertain discrete–time singular Markovian jump systems with time–varying delays

• Published in: IET control theory & applications Vol. 18; no. 8; pp. 987 - 997
• Main Authors: Chen, Wenbin, Gao, Fang
• Format: Journal Article
• Language: English
• Published: Wiley 01.05.2024
• Subjects: asymptotic stability; discrete time systems; robust control
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/cth2.12634

The stabilization problem for uncertain discrete‐time singular Markovian jump systems (DSMJSs) with time‐varying delays is comprehensively covered in this paper. An updated Lyapunov–Krasovskii functional is presented via a discrete state decomposition method. With the help of this constructed Lyapunov–Krasovskii functional, some delay‐ and mode‐dependent sufficient conditions for the open‐loop DSMJSs are derived. Based on these circumstances, a memory mode‐dependent state feedback control is used to create a closed‐loop DSMJS with parameter uncertainties that is regular and causal. And then, the stochastically admissible conditions are attained. Through the exact calculation of each decomposition component for the designed memory state feedback controller, the intended memory state feedback controller settings are determined. It should be mentioned that the algorithm suggested in this article expands the controller design's feasibility and flexibility. The numerical results show how the approach is superior to previous ones, and the given results are less conservative. This paper covers in detail the stabilization issue for uncertain discrete‐time singular Markovian jump systems with time‐varying delays. The derived results are less conservative than the existing ones and numerical examples are given to illustrate the effectiveness of our theoretical results.