Sufficient Stability Conditions of Nonlinear Differential Systems Under Impulsive Control With State-Dependent Delay

In this technical note we study the delayed impulsive control of nonlinear differential systems, where the impulsive control involves the delayed state of the system for which the delay is state-dependent. Since the state dependence of the delay makes the impulsive transients dependent on the historical information of the states, which means that it is hard to know exactly a priori how far in the history the information is needed, the main challenge is how to determine the historical states. We resolve this challenge and establish some sufficient conditions for local stability of nonlinear differential systems with state-dependent delayed impulsive control based on impulsive control theory. Two examples are given to show the effectiveness of the proposed approach.