Synchronization of coupled nonlinear oscillators via regional pole placement technique

This paper is concerned with synchronization of nonlinear oscillators asymmetrically coupled over a time-invariant directed graph. Based on a regional pole placement technique, we design coupling weights which achieve the synchronization by placing the eigenvalues of the weighted Laplacian into a proper convex region on the complex plane. We also extend the present method to the problem of synchronizing within a prescribed settling time. Numerical examples are also included to verify the applicability of the present methods.