Exponential Stabilization of Discrete-time Delayed Systems under Event-triggered Aperiodic Intermittent Control

This paper studies the exponential stabilization of discrete-time delayed systems under event-triggered aperiodic intermittent controls. For discrete-time delayed systems (DDSs), an event-triggered aperiodic intermittent control (EAPIC) scheme and an EAPIC based on state control width (EAPIC-SCW) scheme are designed, respectively. Under the EAPIC scheme, by applying thresh-old and detection period index, an algorithm for event-triggered aperiodic intermittent control is given, and the exponential stability criterion is derived. In addition, an EAPIC-SCW scheme is designed by introducing free control indicators into EAPIC. It is theoretically proved that the designed EAPIC and EAPIC-SCW are non-trivial and can achieve the required exponential stability of the discrete-time delayed system. To assess the performance of these schemes, control times and minimal rate of control are compared between the periodic intermittent control scheme and the time-triggered aperiodic intermittent control scheme. Our theoretical results show that both event-triggered controls offer lower control times and rates. Theoretical results show that both the control times and minimum control rates of the two kinds of event-triggered aperiodic intermittent control are lower. Finally, a numerical simulation example is used to verify the effectiveness of the theoretical results. The results show that the control times and control rates of EAPIC and EAPIC-SCW in 100 seconds are 10 times, 56% and 12 times, 38%, respectively, which are lower than that of the periodic intermittent control and the time-triggered aperiodic intermittent control, and EAPIC-SCW achieves the lowest control rate and the shortest total control time.