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In this paper, we first introduce a more general model of complex dynamical networks with coupling delays and delays in the dynamical nodes than before. Then we further study the synchronization analysis of the complex dynamical networks with coupling delays and delays in the dynamical nodes. Via the theory of Lyapunov-Krasovskii stability and linear matrix inequality (LMI) technique, we investigate the sufficient conditions about synchronization criteria by constructing appropriate Lyapunov functions. The new delay-dependent conditions presented in the paper are formulated in the form of LMI, which can be solved easily by the LMI toolbox in Matlab. The node dynamic need not satisfy the very strong and the matrix is not assumed to be symmetric or irreducible. Moreover, the resulting for network synchronization are expressed in simple forms that can be readily applied in practical situations. The numerical example of the synchronization problem between the nonlinear electromechanical transducers has been investigated, which demonstrate the effectiveness of proposed results. Keywordscomplex networks; coupling delays; delayed nodes; synchronization; linear matrix inequality

Synchronization Analysis of General Complex Dynamical Networks with Couplings Delays and Delays in the Dynamical Nodes