Sliding-Mode Control for Linear Uncertain Systems With Impulse Effects via Switching Gains

• Published in: IEEE transactions on automatic control Vol. 67; no. 4; pp. 2044 - 2051
• Main Authors: Chen, Wu-Hua, Deng, Xiaoqing, Zheng, Wei Xing
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-04-2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Control systems; Dynamic stability; Impulses; Impulsive systems; Liapunov functions; Linear matrix inequalities; linear matrix inequality (LMI); Mathematical analysis; Robust control; Robustness; Sliding mode control; sliding-mode control (SMC); Stability analysis; Switches; Switching; Symmetric matrices; time-dependent lyapunov functional; Trajectory; Uncertain systems
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2021.3073099

This article addresses the problem of sliding-mode control (SMC) of linear uncertain systems with impulse effects. The difficulty in solving such problem lies in that the continuity property of the well-used linear sliding function is lost under the intermittent impulsive action. In order to overcome this difficulty, a piecewise linear sliding function considering the dynamics properties of impulses is introduced, which turns out to be continuous along the trajectories of the impulsive system. Then, a suitable integral SMC law with switching feedback gains is constructed to guarantee the reachability of the designed sliding surface in a finite time. The resulting sliding-mode dynamics is modeled by an impulsive switched system whose stability is analyzed by applying a piecewise discontinuous Lyapunov function. Next, a sufficient condition for the existence of integral SMC law is derived in terms of linear matrix inequalities. Finally, a numerical example with several different types of impulses is provided to validate the theoretical results, which shows that the switching gain-based design contributes to the robustness of the sliding-mode controller.