Robust $\mathcal{H}_{\infty}$ decentralized dynamic control for synchronization of a complex dynamical network with randomly occurring uncertainties

This paper considers synchronization problem of an uncertain complex dynamical network. The norm-bounded uncertainties enter into the complex dynamical network in randomly ways, and such randomly occurring uncertainties (ROUs) obey certain mutually uncorrelated Bernoulli distributed white noise sequences. Under the circumstances, a robust $\mathcal{H}_{\infty}$ decentralized dynamic feedback controller is designed to achieve asymptotic synchronization of the network. Based on Lyapunov stability theory and linear matrix inequality (LMI) framework, the existence condition for feasible controllers is derived in terms of LMIs. Finally, the proposed method is applied to a numerical example in order to show the effectiveness of our result.

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