期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 67, 期 4, 页码 2044-2051出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2021.3073099
关键词
Symmetric matrices; Uncertain systems; Switches; Trajectory; Sliding mode control; Robustness; Linear matrix inequalities; Impulsive systems; linear matrix inequality (LMI); sliding-mode control (SMC); time-dependent lyapunov functional; uncertain systems
资金
- National Natural Science Foundation of China [61633011, 61973095]
- Guangxi Natural Science Foundation [2018GXNSFDA281055]
- Innovation Project of Guangxi Graduate Education [YCSW2020065]
This article addresses the problem of sliding-mode control of linear uncertain systems with impulse effects. It introduces a piecewise linear sliding function considering the dynamics properties of impulses, and constructs a suitable integral sliding-mode control law. The stability of the resulting sliding-mode dynamics is analyzed using a piecewise discontinuous Lyapunov function.
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.
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