Fixed-Time Synchronization of Complex Dynamical Networks: A Novel and Economical Mechanism

Fixed-time synchronization of complex networks is investigated in this article. First, a completely novel lemma is introduced to prove the fixed-time stability of the equilibrium of a general ordinary differential system, which is less conservative and has a simpler form than those in the existing literature. Then, sufficient conditions are presented to realize synchronization of a complex network (with a target system) within a settling time via three different kinds of simple controllers. In general, controllers designed to achieve fixed-time stability consist of three terms and are discontinuous. However, in our mechanisms, the controllers only contain two terms or even one term and are continuous. Thus, our controllers are simpler and of more practical applicability. Finally, three examples are provided to illustrate the correctness and effectiveness of our results.

Automated summary

This article investigates fixed-time synchronization of complex networks. A novel lemma is introduced to prove the fixed-time stability of equilibrium of a general ordinary differential system, and sufficient conditions are presented for synchronization of a complex network using simple controllers. The controllers in this study are simpler, more practical, and have been illustrated through three examples.