Stability of impulsive dynamical networks with different impulse time sequences and application to event-triggered impulsive control.

• The global uniform exponential stability is established for zero-order delayed systems. • The stability results for impulsive dynamical networks are obtained. • The event-triggered impulsive control (ETIC) is designed to stabilize dynamical networks. • ETIC has lower impulse frequency and control cost than the classic impulsive control. • A non-instantaneous ETIC is proposed to improve the instantanity and discontinuity of ETIC. This paper studies the stability for impulsive dynamical networks (IDN) where different nodes may have different impulse time sequences. By deriving the conditions of global uniform exponential stability for zero-order delayed systems, the criteria of stability for IDN are established. The stability results for IDN are then used to design event-triggered impulsive control (ETIC) for stabilization of continuous-time dynamical networks (CDN). In every node of CDN, three levels of event-triggering conditions are set for ETIC. The exponential stabilization of CDN is shown to be achieved by the designed ETIC and it also shows that the ETIC is robust w.r.t. time-delays. Moreover, a non-instantaneous ETIC (NI-ETIC) is proposed for the stabilization of CDN. Three examples with numerical simulations are given to show that the designed ETIC has lower impulse frequency and cost of control than the classic time-triggered impulsive control. It is also shown that the discontinuity and the instantanity of ETIC are improved by the NI-ETIC. [ABSTRACT FROM AUTHOR]