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This paper introduces a general model of complex dynamical networks with coupling delays and delays in the dynamical nodes. The synchronization control of the complex dynamical networks with coupling delays and delays in the dynamical nodes has been studied. Via the theory of Lyapunov-Krasovskii stability and linear matrix inequalities (LMIs) technique, we design the linear feedback synchronization controller for the coupling coefficients known by constructing appropriate Lyapunov functions, which can be solved easily by the LMI toolbox in MATLAB. The controller is very useful for understanding the mechanism of synchronization in complex dynamical networks with coupling delays and delays in the dynamical nodes. It should be pointed out that 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 control problem has been illustrated how to this theorem can be applied to judge and achieve synchronization in complex networks with coupling delays and delays in the dynamical nodes. Keywordscomplex networks; coupling delays; delayed nodes; synchronization control; linear matrix inequalities (LMIs)

Synchronization Control of General Delayed Complex Networks Via LMI Approach