Input-to-state stability of nonlinear systems with delayed impulse based on event-triggered impulse control

This paper investigates input-to-state stability (ISS) of nonlinear systems with delayed impulse under event-triggered impulse control, where external inputs are different in continuous and impulse dynamics. First, an event-triggered mechanism (ETM) is proposed to avoid Zeno behavior. In order to ensure ISS of the considered system, the relationship among event triggering parameters, impulse intensity, and impulse delay is constructed. Then, as an application, ETM and impulse control gain for a specific kind of nonlinear systems are presented based on linear matrix inequalities (LMI). Finally, two examples confirm the feasibility and usefulness of the proposed strategy.