SMC for Discrete-Time Nonlinear Semi-Markovian Switching Systems With Partly Unknown Semi-Markov Kernel

• Published in: IEEE transactions on automatic control Vol. 68; no. 3; pp. 1855 - 1861
• Main Authors: Qi, Wenhai, Zong, Guangdeng, Hou, Yakun, Chadli, Mohammed
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers
• Subjects: Automatic; Density functional theory; Discrete time systems; Discrete-time sliding mode control (DSMC); Engineering Sciences; Kernel; Kernels; mean square stability; Nonlinear control; partly unknown semi-Markov kernel (SMK); semi-Markovian switching systems (S-MSSs); Sliding mode control; Stability criteria; Switches; Switching; Switching systems; Uncertainty; Upper bound; Upper bounds; Partly unknown semi-Markov kernel; Mean square stability; Discrete-time sliding mode control; Semi-Markovian switching systems
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2022.3169584

This article is devoted to the discrete-time sliding mode control (DSMC) for nonlinear semi-Markovian switching systems (S-MSSs). Motivated by the fact that the complete information of the semi-Markov Kernel is difficult to be obtained in practical applications, it is recognized to be partly unknown as the most common mean. By utilizing the prior information of the sojourn-time upper bound for each switching mode, sufficient conditions under the equivalent DSMC law are proposed for the mean square stability. Moreover, the designed DSMC law realizes the finite-time reachability of the sliding region, and makes the sliding dynamics converge to the predesignated sliding region in a finite time. In the end, a numerical example and an electronic throttle model are given to validate the proposed control strategy.