Bounded consensus in multi-agent systems of asymmetrically coupled nonidentical agents

This paper investigates consensus problems of multi-agent systems with asymmetrically coupled nonidentical agents in the sense of boundedness. By employing a Lyapunov function associated with the left eigenvector of the Laplacian matrix corresponding to eigenvalue zero and some graph theory, we derive a sufficient condition of global bounded consensus in form of several scalar inequalities. A distributed consensus protocol is then designed by solving a few of lower dimensional linear matrix inequalities. The presented framework for designing protocols is quite simple and of small conservation, without assuming the condition of node balance or calculating the eigenvalues of Laplacian matrix, which can be effectively used to design consensus protocols of various weighted and directed networks.