Stabilization of complex networks under asynchronously intermittent event-triggered control

In this paper, we explore the input-to-state practically exponential stability of complex networks by designing asynchronous aperiodical intermittent dynamic event-triggered control (AAIDE-TC). Diverging from the existing literature, the form of intermittent control considered in this paper is asynchronous; that is, the intermittent control activation time of each node is different. Moreover, the average control rate for intermittent control is adopted, which is less conservative. More importantly, a Lyapunov function is constructed with the aid of an auxiliary function to overcome the difficulty of dealing with asynchronous aperiodical intermittent control. A dynamic variable and exponential function are then introduced into the AAIDE-TC strategy, playing an essential role in reducing event-triggered frequency and enhancing resource utilization efficiency. Furthermore, the event-triggered frequency for each node is designed to be asynchronous. By resorting to the Lyapunov method and graph theory, this paper derives a criterion for the input-to-state practically exponential stability of complex networks. Finally, the above results are applied to oscillator systems, and numerical simulations are presented to demonstrate the feasibility of the obtained results.