Non-fragile sliding mode control of discrete switched singular systems with time-varying delays

• Published in: IET control theory & applications Vol. 14; no. 5; pp. 726 - 737
• Main Authors: Han, Yueqiao, Su, Chun-Yi, Kao, Yonggui, Gao, Cunchen
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 26.03.2020
• Subjects: asymptotic stability; control system synthesis; delays; discrete reaching condition; finite‐time boundedness problems; FTB; full‐order dynamic system; Lyapunov methods; nonfragile sliding mode approach; nonfragile sliding mode control; nonfragile sliding mode controller; reachability analysis; Research Article; singular systems; sliding mode dynamics; sliding surface function; time method; time‐varying delays; time‐varying systems; uncertain systems; variable structure systems; time-varying systems; singular systems; nonfragile sliding mode approach; sliding surface function; reachability analysis; nonfragile sliding mode control; uncertain systems; control system synthesis; asymptotic stability; finite-time boundedness problems; nonfragile sliding mode controller; time method; FTB; delays; sliding mode dynamics; full-order dynamic system; discrete reaching condition; variable structure systems; time-varying delays; Lyapunov methods
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2019.0349

This study tends to solve the $H_{\infty }$H∞ finite-time boundedness (FTB) problems for discrete switched singular systems with time-varying delays via a non-fragile sliding mode approach. The remarkable feature of the provided method is that a new sliding surface function is constructed such that a full-order dynamic system is acquired. Thus, a non-fragile sliding mode controller can be proposed to guarantee the FTB of the dynamic system. Therein, by employing the multiple Lyapunov-like functions and dwell time (DT) method, sufficient conditions and the DT of switching signal are given to ensure the FTB of the sliding mode dynamics. These results are then applied to the $H_{\infty }$H∞FTB issue, being expressed as a solvable optimisation problem. Furthermore, by employing a discrete reaching condition, the proposed sliding mode controller can guarantee the reachability of the quasi-sliding mode. The validity of the proposed theorems is verified through a numerical example.