Robust synchronization of coprime factor perturbed multi-agent systems

This paper deals with robust synchronization of undirected multi-agent networks with uncertain agent dynamics. Given an undirected network with identical nominal dynamics for each agent, we allow uncertainty in the form of coprime factor perturbations of the transfer matrix of the agent dynamics. We assume that these perturbations are stable and have H_∞-norm that is bounded by some a priori given desired tolerance. In this paper, we derive state space equations for dynamic observer based protocols that achieve synchronization in the presence of such perturbations. We show that this robust synchronization of the network by the dynamic protocol is equivalent to robust stabilization of a single linear system by all controllers from a related finite set of feedback controllers. Our protocols are expressed in terms of real symmetric solutions to certain algebraic Riccati equations, and contain weighting factors depending on the eigenvalues of the graph Laplacian. We show that in this class of dynamic protocols, one can achieve a guaranteed tolerance that is proportional to the square root of the quotient of the smallest and the largest eigenvalue of the graph Laplacian.