Multi agent systems with directed communication graph

This study investigates the consensus problem for cooperative heterogeneous agents with non-linear dynamics in a directedcommunication network. Global bounded consensus is studied by employing a quadratic Lyapunov function, and a distributed consensus protocol is designed by solving a few lower-dimension linear matrix inequalities associated with the dynamics of the heterogeneous agents. A sufficient condition corresponding to the semi-positive definiteness of the Laplacian matrix and the non-linear dynamics of each agent is obtained to guarantee the boundedness of consensus.

In particular, to avoid the calculation of matrix eigenvalues, a sufficient condition is also obtained in the form of several scalar inequalities involving the coupling strengths and the property of all paths between agent pairs under a proper path strategy. The presented framework for designing protocols is quite simple with limited conservatism, which can be effectively used to design consensus protocols of various weighted and directed networks.