Average Dwell-Time Conditions for Input-to-State Stability of Impulsive Systems

This paper provides sufficient conditions for input-to-state stability of impulsive control systems on Banach spaces. The derived conditions determine average dwell-time constraints for a candidate Lyapunov function parametrized by a class of nonlinear rate functions in order to guarantee the ISS property. Thereby, we consider a generalized case with unstable continuous flow maps and assume the jumps, rather than the continuous flow to induce a stabilizing influence on the system dynamics of the impulsive system. Compared to some well-known related and recent results in the literature, such as fixed dwell-time conditions, the obtained conditions are more general, while offering a higher flexibility in the choice of candidate Lyapunov functions. Copyright (C) 2020 The Authors.