Dynamic feedback H_∞ control for discrete singular systems with time–varying delays

Abstract

This work carefully revisits the topic of dynamic feedback $H_{\mathrm{\infty }}$ control problem for discrete singular systems (DSSs) with time–varying delays. A new state decomposed Lyapunov-Krasovskii functional is presented by a discrete state decomposition method. For the unforced nominal DSSs, delay–dependent sufficient conditions with an $H_{\mathrm{\infty }}$ performance index are derived. Based on these conditions, a closed–loop system being regular and causal is developed via a dynamic feedback controller. As a new discrete state decomposition–reorganization method is proposed, the required admissibility conditions are attained. Through the accurate calculation of each decomposition component of the dynamic feedback controller, the desired dynamic feedback controller settings are determined. The numerical findings demonstrate the superiority of our method over earlier approachers, and the results are less conservative.

Keywords:

• Discrete singular system
• $H_{\mathrm{\infty }}$ control
• time–varying delay
• admissibility
• dynamic feedback control

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability

Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China under Grant (62103006), the Anhui Province Higher School Science Research Project under Grant (2023AH050140) and the Anhui Provincial Nature Science Foundation under Grant (2308085MF197).