Indefinite Lyapunov functions for input-to-state stability of impulsive systems

This paper presents a new Lyapunov method for the input-to-state stability (ISS) and integral ISS (iISS) of impulsive systems. The approach is proposed on the basis of an indefinite Lyapunov function rather than a negative definite one. When the continuous dynamics have a Lyapunov function with an indefinite time derivative, and the discrete dynamics are destabilizing, the impulsive system is ISS if an average dwell-time (ADT) condition is satisfying. Numerical examples show their effectiveness and advantages.