Synchronization of fractional-order linear complex networks

- A class of fractional-order complex networks with general linear node dynamics are constructed, in which the nodes are interconnected through undirected and weighted coupling topology.
- An effective simultaneous-stabilization-based method combining pseudo-state transformation technique and algebraic graph theory is presented for analyzing synchronization dynamics occurred on such networks.
- Two sufficient criteria for synchronization in terms of linear matrix inequalities (LMIs) are derived for 1≤α<2 and 0<α<1 respectively, which are very convenient to be used in practice with the help of Matlab LMI Toolbox.

In this paper, we concentrate on the synchronization problem of fractional-order complex networks with general linear dynamics under connected topology. By introducing a pseudo-state transformation, the problem is converted into an equivalent simultaneous stabilization problem of independent subsystems, which is characterized by nonzero eigenvalues of the Laplacian matrix. Then, sufficient conditions in terms of linear matrix inequalities (LMIs) for synchronization are established, which can be easily solved by efficient convex optimization algorithms. Finally, three examples are provided to illustrate the effectiveness of the proposed method.