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… Click to show full abstract
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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