Aperiodic event-triggered impulsive control of switched systems based on novel Lyapunov functions with application to PMSM

This paper investigates the input-to-state stability (ISS) of nonlinear impulsive switched systems under aperiodic event-triggered impulsive control. First, a timer-dependent multiple discontinuous Lyapunov function (TMDLF) is constructed by combining a non-isometric partitioning method with a discrete counter function, which obtains less conservative mode-dependent average dwell time (MDADT) constraints. Second, by integrating sampled-data control, event-triggered control, and impulsive control, a novel aperiodic sampling-based event-triggered impulsive mechanism is proposed, achieving dynamic adjustment of sampling intervals. Based on this framework, three important corollaries on input-to-state stability are derived for nonlinear impulsive switched systems under the following scenarios: all modes are stable, all modes are unstable, and the switching sequence is known. Finally, the proposed control strategy is applied to a nonlinear permanent magnet synchronous motor (PMSM), demonstrating its potential and effectiveness.