Consensus of the Leaderless Second-order Heterogeneous Linear Multi-agent System

This paper studies the state consensus problem of a leaderless second-order heterogeneous linear multi-agent system under a fixed directed communication topology. First, this paper proposes a generic consensus protocol with different gain matrices and communication weights in matrix form. Then, this paper adopts a state linear transformation based on a virtual directed spanning tree of the communication topology to convert the consensus problem into a partial variable stability problem. For the second-order systems of general form and a special form, this paper deduces sufficient and necessary consensus criteria in terms of Hurwitz stability of corresponding matrices, respectively. According to these criteria, iterative algorithms are presented to find the gain matrices in the protocol by solving some bilinear matrix inequalities. Finally, the effectiveness of the proposed theoretic results are verified by providing simulation examples of leaderless heterogeneous multi-agent systems in general and special cases.