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**Single impulsive controller for globally exponential synchronization of dynamical networks.**
*(English)*
Zbl 1254.93133

Summary: This paper is devoted to studying the synchronization control of impulsive dynamical networks. A single impulsive controller is proved to be effective for the stabilization of dynamical networks with impulse-coupling. Some simple and easily verified criteria are given for the stabilization of impulsive dynamical networks under a single impulsive controller and/or a single negative state-feedback control. Moreover, the effects of a single impulsive controller, a single state-feedback controller and an isolated dynamical system on the synchronization process are respectively distilled and explicitly expressed in the derived criteria. The structure of the dynamical network can be directed and weakly connected with a rooted spanning tree. Moreover, the convergence rate of the dynamical network is also explicitly estimated, and there is no requirement on the lower and upper bounds of the impulsive intervals. A numerical example is presented to illustrate the efficiency of the designed controller and the validity of the analytical results.