Event-triggered hybrid impulsive control for synchronization of fractional-order multilayer signed networks under cyber attacks.

In this paper, we consider the exponential bipartite synchronization (EBS) problem of fractional-order multilayer signed networks with time-varying delays (FO-MSNT) under random cyber attacks. In contrast to the existing literature, the proposed hybrid event-triggered controller combines the advantages of feedback controller and impulsive controller, and the event-triggered condition is constructed by applying the network topology and the Lyapunov function of the subsystem, rather than the state function of the subsystem. Based on the Lyapunov-Razumikhin method and the graph theory, some sufficient conditions for achieving EBS of FO-MSNT under cyber attacks which are related to the topology of networks, the event-triggered parameters, the order of fractional derivative and the signal sent by the enemy are obtained. Furthermore, fractional-order coupled Chua's circuits model and fractional-order power systems built on MSNT are established and the EBS issues under cyber attacks are analyzed. Numerical examples and simulations are provided to show the validity of our theories.