Class-KL estimates and input-to-state stability analysis of impulsive switched systems

In this paper, we investigate input-to-state stability of impulsive switched systems. The goal is to bridge two apparently different, but both useful, stability notions, input-to-state stability and stability in terms of two measures, in the hybrid systems setting. Based on two class-KL function estimates and a comparison theorem for impulsive differential equations, two sets of sufficient Lyapunov-type conditions for input-to-state stability in terms of two measures are obtained for impulsive switched systems. These conditions exploit some nonlinear integral constraints in terms of generalized dwell-time conditions to balance the continuous dynamics and impulsive dynamics so that input-to-state stability is achieved, despite possible instability of individual continuous subsystems or destabilizing impulsive effects. An illustrative example is presented, together with numerical simulations, to demonstrate the main results. (C) 2012 Elsevier B.V. All rights reserved.