Synchronization Analysis and Verification for Complex Networked Systems Under Directed Topology

This article investigates synchronization analysis and verification for complex networked systems with nonlinear coupling. Based on general Lyapunov functions beyond the quadratic form, a less conservative synchronization criterion is proposed for the nonlinear networked systems under the directed topology. Then, the synchronization problem for polynomial networks can be converted into a sum-of-squares programming problem, which falls within the convex programming framework, yielding polynomial Lyapunov functions efficiently to realize the automatic synchronization verification in polynomial time. Finally, the effectiveness of the theoretical results is demonstrated by a numerical example, in which our proposed method can guarantee to achieve synchronization by using a smaller lower bound of coupling strength.