Event-triggered impulsive control with time delays for input-to-state stabilization of nonlinear systems

The paper examines the input-to-state stability (ISS) in nonlinear impulsive systems under Event-triggered impulsive control (ETIC), which is a method that differs from traditional approaches by activating the controller only when state-dependent event conditions are met and maintains no control action between consecutive impulse instants. The event-triggered mechanism (ETM) generates state-dependent impulses, and time delays in impulses are comprehensively accounted for. The derived sufficient conditions guarantee the exclusion of Zeno behavior and the assurance of the ISS, while considering external inputs in both continuous and impulsive dynamics. A new event-triggered delayed impulsive control (ETDIC) strategy is presented to reveal the relationship among relevant parameters, namely that time delays in impulses may actually promote stabilization in terms of the ISS. Lyapunov-based criteria are established to prevent fast triggering. These results are applied to nonlinear systems to obtain the ETM and control gains via linear matrix inequalities (LMIs). Two numerical examples validate the proposed theory and strategies.