Orbital Control for a Class of Planar Impulsive Hybrid Systems with Controllable Resets

This paper investigates the stabilization of a novel subclass of impulsive hybrid systems (IHS) that feature controllable guards and resets maps. While the structure of the guards and the reset map is assumed to be completely determined from the physical set-up, both mappings are jointly adjustable through exogenous control inputs at run-time. As a core feature, all adjustments result in simultaneous, inseparable changes of the reset time and the reset action. In real world, such systems are encountered in mechanical impact systems. In particular, this paper addresses the task of enforcing global orbital asymptotic stability of given periodic executions by means of dedicated control actions.