Input-to-state Stability of Impulsive Systems with Different Jump Maps

Abstract: The paper introduces sufficient conditions for input-to-state stability (ISS) of a class of impulsive systems with jump maps that depend on time. Such systems can naturally represent an interconnection of several impulsive systems with different impulse time sequences. Using a concept of ISS-Lyapunov function for subsystems a small-gain type theorem equipped with a new dwell-time condition to verify ISS of an interconnection has been proven.