An invariance principle for nonlinear hybrid and impulsive dynamical systems

In this paper we develop an invariance principle for dynamical systems possessing left-continuous flows. As a special case of this result we state and prove new invariant set stability theorems for a class of nonlinear impulsive dynamical systems; namely, state-dependent impulsive dynamical systems. These results provide less conservative stability conditions for impulsive systems as compared to classical results in literature and allow us to address the stability of limit cycles and periodic orbits of impulsive systems.