Sliding mode synchronization of a delayed complex dynamical network in the presence of uncertainties and external disturbances

This paper is concerned with the problem of robust sliding mode H ∞ control of a delayed complex dynamical network subject to parametric uncertainties and external disturbances. In this regard, synchronization error dynamics between the nodes of the complex dynamical network and an individual node are derived. Based on Lyapunov–Krasovskii stability theory, sliding mode H ∞ control laws are designed to force the state trajectories of the error dynamics to sliding manifolds and are maintained thereafter. Moreover, an H ∞ control law is designed to compare its results with the proposed method. By simulating a numerical Chua’s circuit, it is shown that the proposed method is effective at attenuating the effect of the external disturbances and parametric uncertainties.

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