| Abstract: | We deal with the state consensus problem of a general Linear Interconnected Multi-Agent System(LIMAS) under a time-invariant and directed communication topology.Firstly,we propose a linear consensus protocol in a general form,which consists of state feedback of the agent itself and feedback form of the relative states between the agent and its neighbors.Secondly,a state-linear-transformation is applied to equivalently transform the state consensus problem into a partial stability problem.Based on the partial stability theory,we derive a sufficient and necessary criterion of consensus convergence,which is expressed via the Hurwitz stability of a real matrix constructed from the parameters of the agent models and the protocols,and present an analytical formula of the consensus function.Lastly,we propose a design procedure of the gain matrices in the protocol by solving a bilinear matrix inequality. |
