Impulsive synchronization of higher-order network with multiple delays

This paper mainly investigates the issue of synchronization of higher-order networks with multiple delays via impulsive control. To achieve synchronization, an impulsive control scheme is adopted to devise effective controllers. On the basis of Laypunov function and mathematical analysis theory, sufficient conditions for a higher-order network to realize impulsive synchronization with multiple time delays are given. This result extends the one-order network to higher-order network, and takes into account the case of multiple time delays. Furthermore, the adaptive strategy is utilized to alleviate the constraints on impulsive intervals and impulsive gains, reduce the cost of network control and make the conditions more universal. Impulsive instants can be approximated through solving a series of maximum problems, and the impulsive gains can converge to a needed value. Ultimately, the credibility of the theoretical results is substantiated through numerical simulations.