Robust Consensus for a Class of Uncertain Multi-Agent Dynamical Systems

This paper investigates robust consensus for a class of uncertain multi-agent dynamical systems. Specifically, it is supposed that the system is described by a weighted adjacency matrix whose entries are polynomial functions of an uncertain vector constrained in a semi-algebraic set. For this uncertain topology, we provide necessary and sufficient conditions for ensuring robust first-order consensus and robust second-order consensus, in both cases of positive and non-positive weighted adjacency matrices. Moreover, we show how these conditions can be investigated through convex programming by using standard software. Some numerical examples illustrate the proposed results.