Intermittent adaptive dynamic event-triggered control for exponential synchronization of multi-links time-delayed stochastic complex networks with Markovian switching

This paper focuses on the issue of the exponential synchronization in mean square (ESMS) of the multi-links time-delayed stochastic complex networks with Markovian switching (MTSCNM) through a novel intermittent adaptive dynamic event-triggered control (IADE-TC). First of all, the parameters within the event-triggered condition of the IADE-TC mechanism are associated with the adaptive strength, signifying that the event-triggered condition can be adjusted as the systems evolve to enhance its flexibility. Additionally, with the aim of potentially further reducing the number of the event-triggered instants, the dynamic variable is designed to increase within the rest intervals when the intermittent controller is not in operation. Then, by applying the graph theoretic approach and the Lyapunov functional method, the sufficient conditions for ESMS of MTSCNM are obtained. Furthermore, it is proved that the Zeno behavior does not arise under the IADE-TC. Finally, the ESMS of the multi-links time-delayed stochastic oscillator system is discussed and a numerical simulation is carried out to validate the effectiveness of the main results.