Abstract
In this paper we study the pinning controllability of networks when noise affects either the node dynamics, or the communication links or the connections through which pinning control itself is being exerted. By using appropriate Lyapunov functions and the notion of almost sure exponential stability, we provide simple algebraic conditions depending on the node dynamics, networks structure, noise intensity and control parameters to guarantee that the network states converge toward the desired trajectory. Rather than observing noise to be detrimental for achieving control of the network collective behaviour, we find that under some specific conditions noise can enhance the pinning controllability of the network, making it easier to drive all network nodes towards the desired collective evolution of interest. Throughout the paper, theoretical results are illustrated via representative numerical examples showing the effectiveness of the proposed approach.
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