Sliding mode control for linear uncertain systems with impulse effects via switching gains

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.