Input-to-state stability of nonlinear impulsive systems via Lyapunov method involving indefinite derivative

This paper investigates the input-to-state stability (ISS) and integral-input-to-state stability (iISS) of nonlinear impulsive systems. By using Lyapunov method involving indefinite derivative and average dwell-time (ADT) method, some sufficient conditions for ISS are obtained, where both types of impulses, stabilizing impulses and destabilizing impulses, are considered. In our approach, the time-derivative of the Lyapunov function is not necessarily negative definite, that allows wider applications than existing results in the literature. Several illustrative examples are presented, with their numerical simulations, to demonstrate the main results.