Stabilisation to input-to-state stability for continuous-time dynamical systems via event-triggered impulsive control with three levels of events

This study investigates the issue of stabilisation to input-to-state stability (ISS) by event-triggered impulsive control (ETIC) for continuous-time dynamical systems (CDSs) with external inputs/disturbances. The CDSs are more general systems with possible multiple vector fields and dynamics. The ETIC scheme is based on three key indices: threshold value, control-free index, and check period, and it is executed by designing three levels of events from which ETIC is triggered. Both ETIC and ETIC with time-delays (delayed ETIC) are studied, respectively, and the criteria for ISS are derived for CDSs under ETIC. Thus the stabilisation to ISS is achieved for CDSs by the designed ETIC with or without time delays. The data dropout of ETIC is also investigated, where the maximal allowable dropout rates are estimated, respectively. It shows that the proposed ETIC scheme has advantages over the reported event-triggered control and has robustness with respect to the network-induced time-delays although larger time-delays might lead to a slower convergence speed for the stabilisation to ISS. Finally, two examples with numerical simulations are given to illustrate the obtained results.