Designing synchronization protocols in networks of coupled nodes under uncertainty

This paper considers the problem of synchronizing the outputs of nodes in a network of N coupled dynamical systems in the presence of uncertainty. A computational approach is used to design coupling dynamics that ensure synchrony when nodes are subject to model uncertainty and that minimize nodal deviation from synchrony in the presence of input noise. The main result of this paper recasts the problem of designing the coupling a robust stability problem with a structured uncertainty element. A coupling satisfying the criteria of this robust stability problem can then be designed through an application of the small-gain theorem and μ-synthesis techniques.