Distributed Pinning Impulsive Control for Inner–Outer Synchronization of Dynamical Networks on Time Scales

In this paper, inner–outer synchronization problem of dynamical networks on time scales is studied. This kind of network synchronization means that two dynamical networks can achieve inner/outer synchronization simultaneously. By designing suitable distributed pinning impulsive controllers, the inner–outer synchronization target is realized. Based on the Lyapunov function method and the mathematical induction approach, two sufficient criteria are given for inner–outer synchronization of two networks with identical and non-identical topologies. Due to the structure of time scales, the derived results can be applied to study the inner–outer synchronization problems of continuous/discrete networks and networks on hybrid time domains. A numerical simulation example is given to illustrate the effectiveness of the derived results.