Event-Based Time-Interval Pinning Control for Complex Networks on Time Scales and Applications

This paper studies the synchronization problem for linear complex dynamical networks (CDNs) on time scales. An intermittent dynamic time-interval pinning control strategy is designed to achieve synchronization for CDNs with the isolated node. Based on the Lyapunov approach and the theory of time scales, synchronization criteria are established for CDNs on general time scales. The main results in the paper show that, by controlling a proportion of the network nodes, the exponential synchronization can be achieved. Moreover, the infinitely fast switching of the pinning node set is avoided by means of the event-triggered strategy. According to our selection algorithm, the number of pinning nodes will be updated online at each pinning time. The modeling framework investigated in this paper is a unification and generalization of many existing continuous-time and discrete-time complex network models. Three numerical examples are given to illustrate the effectiveness and priority of the obtained results. Finally, the analytical results are applied to the distributed auxiliary control of microgrids and formation control of spacecraft.