On robust forward invariance of sets for hybrid dynamical systems

Abstract

Forward invariance with robustness to disturbances for hybrid dynamical systems modeled by hybrid inclusions with state-dependent conditions enabling flows and jumps is studied. In particular, we study forward invariance notions that apply to systems with hybrid inputs and disturbances with nonlinear dynamics, for which not every solution is unique or may exist for arbitrary long hybrid time. Given state-feedback laws, notions of robust forward invariance of sets for closed-loop system are introduced. Sufficient conditions in terms of the objects defining the system are presented. One result using Lyapunov-based conditions removes the usual Lipschitz constraint on continuous dynamics. A bouncing ball example is given to illustrate major results.