Sliding-Mode Control for Slow-Sampling Singularly Perturbed Systems Subject to Markov Jump Parameters

• Published in: IEEE transactions on systems, man, and cybernetics. Systems Vol. 51; no. 12; pp. 7579 - 7586
• Main Authors: Wang, Jing, Yang, Chengyu, Shen, Hao, Cao, Jinde, Rutkowski, Leszek
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Circuit stability; Circuits; Control stability; Control systems design; Markov jump systems (MJSs); Markov processes; Parameters; Sampling; singularly perturbed systems (SPSs); Sliding mode control; sliding-mode control (SMC); Stability analysis; Surface stability; Surface treatment; Symmetric matrices; Trajectory
• ISSN: 2168-2216; 2168-2232
• DOI: 10.1109/TSMC.2020.2979860

This article addresses the investigation of sliding-mode control (SMC) for slow-sampling singularly perturbed systems (SPSs) with Markov jump parameters. As a new attempt, the SMC strategy is considered in the study of discrete-time Markov jump SPSs. Subsequently, in order to design a sliding-mode controller to ensure the stability of the proposed system, a novel integral sliding surface is constructed, and an SMC law is synthesized to ensure the reachability of the sliding surface. Through the utilization of Lyapunov stability and SMC theory, sufficient conditions are derived to ensure the state trajectories of the system are driven to a predefined sliding surface and the closed-loop sliding mode dynamics are stochastically stable. Finally, the applicability of the proposed SMC strategy is verified by a numerical example and a practical electric circuit model.