Event-triggered communication for synchronization of Markovian jump delayed complex networks with partially unknown transition rates

• The network model in this paper involves time delay and partly unknown transition rates, which is more practical than the models in [18], [34], [35] and [38].
• Different from the most existing results with partly unknown transition rates [24], [25] and [26], the synchronization trajectory in this paper is dynamic, which will be adjusted according to the states of nodes.
• A randomly occurring event-triggered control strategy is proposed to study the synchronization issue of Markovian jump delayed complex networks with partly unknown transition rates.
• The positive lower bound of the event intervals is obtained which can exclude undesired accumulation of event instants (Zeno behaviors).

In this paper, exponential synchronization problems are investigated for an array of Markovian jump delayed complex networks with partially unknown transition rates and discontinuous diffusions. To impel the array complex networks to achieve exponential synchronization, a new randomly occurring event-triggered control strategy is proposed. The idea of event-triggered control strategy is that the coupling term and controller update data only at the event-triggered instants, which can reduce the communication load and energy consumption. By constructing a novel stochastic Lyapunov–Krasovskii function, some exponential synchronization criteria are obtained in terms of LMIs and famous Halanay inequality. Furthermore, we obtain a positive lower bound of the event intervals which can exclude the Zeno behaviors. Finally, a simulation example is given to illustrate the effectiveness of the theoretical results.