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.
