Fixed-Time and Predefined-Time Stability of Impulsive Systems

Several criteria for fixed-time stability and predefined-time stability of impulsive systems are established. First, sufficient conditions for fixed-time stability of impulsive systems are presented to treat the destabilizing impulses and hybrid impulses involving multiple jump maps by fixed-time control without linear feedback regulation. It determines the robustness of nonlinear systems against impulsive disturbance which has destabilizing and hybrid effect to dynamics. Then, the predefined-time stability of impulsive systems is ensured under the requirement that the hybrid impulses have stabilizing accumulative effect. Finally, the validity of theoretical results is verified by the allocation of mobile agents on a segment via fixed-time control with impulsive regulation.