Abstract

This chapter studies the input-to-state stability (ISS) property for nonlinear control systems with impulsive jumps at fixed moments. Sufficient conditions for the ISS are formulated in terms of a candidate ISS-Lyapunov function equipped with nonlinear rate functions which characterize the evolution of this function along the discontinuous trajectories of the system. For the case of unstable continuous dynamics, we derive new sufficient conditions for ISS under average-type dwell-time that provide a lower bound for the frequency of stabilizing jumps sufficient for the ISS.

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