The Exponential ISS Stability for Nonlinear Impulsive Hybrid Systems

This paper introduces appropriate concepts of input-to state stability (ISS) for nonlinear impulsive hybrid systems(NIHS). First we study the case in which one kind of dynamics system without external inputs has a stability property, then by applying the ISS-Lyapunov function theory, several sufficient conditions are derived for the ISS property of the whole NIHS with inputs. The results of ISS are used to study the robustly globally uniformly exponential stability for impulsive hybrid systems. The impulsive hybrid system can keep ISS no matter how often the impulses occur. Our proposed results are evaluated using illustrative example to show their effectiveness.