Stability of Nonlinear Impulsive Systems: Self-Triggered Comparison System Approach

This article presents a new approach to the problem of globally asymptotical stability for nonlinear impulsive systems by utilizing self-triggered impulsive control (STIC), where impulse instants are determined by a well-designed self-triggered mechanism, which is based on the comparison approach. Different from event-triggered impulsive control strategy in which the triggering conditions need to be continuously or periodically monitored to determine whether an impulse should be generated, our proposed STIC strategy does not require those monitoring because it can utilize the measurable information to predict the next impulse instant. Based on the proposed STIC strategy, some Lyapunov-based sufficient conditions for globally asymptotical stability are derived by adopting the comparison approach. Moreover, we prove that the Zeno behavior can be excluded from our results. Specifically, we apply the theoretical results to resolve the STIC problem for a class of nonlinear systems, where two different cases are fully considered, that is, state-based STIC and output-based STIC. For each case, the design method of STIC strategy is given in terms of linear matrix inequalities. The effectiveness of the proposed methods is verified by two numerical examples and their simulations.