Fixed-Time Discontinuous Control for Cluster Secure Synchronization of Interlayer Switching Networks Under Attacks

This paper mainly concentrates on the issue of fixed-time cluster secure synchronization upon interlayer switching networks with DoS attacks, in which the DoS attacks may cause random damage to the nodes/edges in networks and then generate impulsive disturbances. To resist the attacks, one robust fixed-time discontinuous control strategy is proposed, such that all the nodes in interlayer switching networks can achieve the cluster secure synchronization even when the communication topology are disconnected or changed over time after being influenced by attacks. By using the Lyapunov method, several effective conditions for fixed-time cluster secure synchronization and the maximum convergence time near to the actual value are obtained. In view of the comparison principle, a suitable estimation method upon stability time for the switching networks is established, and the stability time is computable and controllable. Moreover, the correlation among attack intensity, connectivity network, impulsive interval, impulsive disturbance intensity and synchronization time is revealed. Simulation case is finally supplied to manifest the availability of the obtained outcomes.