Successive lag synchronization on nonlinear dynamical networks via linear feedback control

Successive lag synchronization (SLS) is defined as a new synchronization pattern, which means that lag synchronization appears between two successively numbered nodes in a dynamical network. Based on the topological structure of the considered network, linear feedback control and adaptive linear feedback control are proposed to achieve the SLS. By using Lyapunov function method and Barbalat Lemma, some sufficient conditions for the global stability of SLS are obtained. Moreover, the stability condition is independent on time delay. By using the proposed control method, successive lag consensus of a multi-agent system with second-order dynamics is also realized. By utilizing the Chua’s circuit as the local nonlinear dynamics of all nodes in the network, several numerical examples are presented to verify the theoretical results.

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