H ∞ consensus regions of multi-agent systems

This paper addresses the distributed H ∞ consensus problem of linear or linearized multi-agent systems subject to external disturbances. A distributed consensus protocol is proposed, based on the relative states of neighboring agents. The distributed H ∞ consensus problem of such a multi-agent network is cast into the H ∞ control problem of a set of independent systems having the same dimension as that of a single agent. The notion of H ∞ consensus region is then introduced and analyzed. A necessary and sufficient condition for the existence of a protocol having an unbounded H ∞ consensus region is derived. A multi-step procedure is further presented for constructing such a protocol. It is shown that the H ∞ performance limit of the consensus of the multi-agent network is equal to the minimal H ∞ norm of a single agent achieved by using a state feedback controller.