Output consensus of linear multi-agent systems: Linear-transformation-based partial stability approach

This paper deals with the output consensus problem of high-order linear multi-agent systems. A generalized linear protocol is proposed, which consists of a state feedback of the agent itself and a cooperative protocol in a generalized feedback form of the relative states between the agents. Then a state-linear-transformation is constructed to transform the output consensus problem into a partial stability problem. Based on the partial stability theory, a necessary and sufficient criterion is provided for the linear multi-agent system achieving output consensus, which is expressed in terms of Hurwitz stability of a real matrix constructed from the parameters of the agent models and the protocol.