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The problem of synchronization of systems over a network, is a widely studied problem given the importance of synchronization phenomena, in various natural science and engineering applications. In this paper, we study one of the important aspect of this problem that is, robustness of synchronization to random link failure uncertainty. The link failure uncertainty is modeled as an on-off Bernoulli switch. The main results of this paper provide, for the first time, analytical conditions for the maximum tolerable link failure uncertainty to maintain mean square synchronization among the network components. The analytical conditions are expressed in terms of individual component dynamics, network properties, and link uncertainty. The main results of this paper can be used to determine, the weakest/strongest link in the network. Simulation results are provided to verify the main results of this paper.

SUMMARYIn this paper, we study the problem of control of discrete‐time linear time varying systems over uncertain channels. The uncertainty in the channels is modeled as a stochastic random variable. We use exponential mean square stability of the closed‐loop system as a stability criterion. We show that fundamental limitations arise for the mean square exponential stabilization for the closed‐loop system expressed in terms of statistics of channel uncertainty and the positive Lyapunov exponent of the open‐loop uncontrolled system. Our results generalize the existing results known in the case of linear time invariant systems, where Lyapunov exponents are shown to emerge as the generalization of eigenvalues from linear time invariant systems to linear time varying systems. Simulation results are presented to verify the main results of this paper. Copyright © 2012 John Wiley & Sons, Ltd.