Distributed quadratic stabilization of uncertain linear multi-agent systems

This paper considers the distributed quadratic stabilization problems of uncertain continuous-time linear multi-agent systems with undirected communication topologies. It is assumed that the agents have identical nominal dynamics while subject to different norm-bounded parameter uncertainties, leading to weakly heterogeneous multi-agent systems. A distributed controller is proposed, based on the relative states of neighboring agents and a subset of absolute states of the agents. It is shown that the distributed quadratic stabilization problem under such a controller is equivalent to the H_∞ control problems of a set of decoupled linear systems having the same dimensions as a single agent. A two-step algorithm is presented to construct the distributed robust controller, which does not involve any conservatism and meanwhile decouples the feedback gain design from the communication topology. Furthermore, the distributed quadratic H_∞ control problem of uncertain linear multi-agent systems with external disturbances is discussed, which can be reduced to the scaled H_∞ control problems of a set of independent systems whose dimensions are equal to that of a single agent.