Eigenvalue-based approach to global consensus of nonlinear multi-agent systems

This paper investigates the global consensus of asymmetrically coupled multi-agent systems with nonlinear dynamics. By employing a Lyapunov function, a consensus criterion is presented by checking an inequality involving the smallest eigenvalue except zero of a redefined symmetric matrix associated with the asymmetric Laplacian matrix to guarantee the global consensus of the considered multi-agent systems. In particular, we show that the presented criterion is equivalent to the result by defining a generalized algebraic connectivity [21] corresponding to the Laplacian matrix. Numerical simulations are carried out to demonstrate the effectiveness of the proposed method.