Robust H_∞Consensus for Homogeneous Multi-agent Systems with Parametric Uncertainties

This paper addresses the problem of robust consensus of an undirected network of homogeneous multi-agent systems with uncertain agent dynamics and system noise. We consider uncertain time-varying input matrices that are arbitrary up to a known bound for the singular values. We also assume that each agent's controller is able to access the neighbors' relative states. We focus on the design of a linear controller gain that is to be identical across all agents. We provide sufficient conditions for the control gains to achieve both consensus in the noiseless setting and a transfer function with a given bounded H∞ norm in the setting with noise. More specifically, we show that this is achieved if a set of linear matrix inequalities containing the non-zero eigenvalues of the Laplacian are satisfied. In a numerical simulation, we illustrate these theoretical results and show that our method outperforms a consensus region-based approach.