Consensus of Second-order Heterogeneous Linear Multi-agent Systems

This paper explores the leader-following consensus of second-order heterogeneous linear multi-agent systems with the directed communication topology. Firstly, we propose a general consensus algorithm which composed of different gain matrices and generic communication matrices, which increases the system freedom degree. Then, we adopt the state linear transformation method to convert the consensus study to a partial variable stability study of the corresponding auxiliary system, thereby reducing the computation complexity of the research problem. On this basis, we get a sufficient and necessary consensus standard. According to this criterion, by solving bilinear matrix inequality, we propose an algorithm for solving the protocol gain matriies. Finally, two sets of simulations prove the effectiveness of the algorithm proposed in this paper.