Observer-based sliding mode control of impulsive systems with unknown mismatched disturbances

This paper studies a novel observer-based sliding mode control problem for impulsive systems involving unknown mismatched disturbances. Different from the existing sliding mode control coupling the complete information of known disturbances, our proposed observer-based sliding mode control depends on the disturbance estimation and incorporates the bound of disturbance estimation error into the switch gain design. It is shown that the proposed observer-based sliding mode control not only implicitly restrains the negative effects of unknown mismatched disturbances, but also ensures the reachability of the designed sliding surface in a finite time. Some reachability criteria of impulsive systems are established, where a potential relationship between mismatched disturbances, impulse actions, and sliding function is presented. This relationship fully estimates the effects of discrete dynamics and avoids the resulting sliding mode dynamics jumping out of the designed sliding surface at impulse instants. Following that, some linear matrix inequalities-based conditions are obtained to stabilize the resulting sliding mode dynamics. Finally, two examples are provided to verify our results, including the one focusing on the mass–spring-damper systems.