Event-triggered impulsive control for nonlinear delay systems

This paper studies the exponential stability of nonlinear delay systems by means of event-triggered impulsive control (ETIC) approach, where impulsive instants are determined by a Lyapunov-based event-triggered mechanism (ETM). Based on the ETM, sufficient conditions are presented to exclude Zeno behavior and guarantee the exponential stability in the framework of Lyapunov–Razumikhin method. Different from time-triggered impulsive control in which the triggered time is determined artificially, ETIC is activated only when some well-designed events occur. Moreover, control input is only needed at triggered instants and there is no any control input during two consecutive triggered instants. As an application, the theoretical result is applied to nonlinear delay multi-agent systems. A class of ETIC strategies is designed to achieve consensus of the addressed systems. Finally, two numerical examples are presented to illustrate the effectiveness of the developed approach.