Stability for nonlinear delay systems: Self-triggered impulsive control

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This paper studies the stability problem of nonlinear delay systems in the framework of self-triggered impulsive control (STIC), where a class of self-triggered mechanisms is designed based on comparison approach. Different from the traditional event-triggered impulsive control (ETIC), in this paper the next impulse instant can be predicted at the previous impulse instant, and there is no need for state monitoring between two adjacent impulse instants. Under the proposed STIC strategy, some sufficient conditions for non-Zeno behavior and asymptotical stability of nonlinear delay systems are presented, respectively. Finally, two numerical examples are carried out to illustrate the effectiveness of the theoretical results.