Prescribed-Time Synchronization of Multiweighted and Directed Complex Networks

TL;DR

This paper introduces a novel prescribed-time synchronization method for complex networks with multiweights and directed links, allowing synchronization at a preset time regardless of initial conditions or parameters.

Contribution

It develops a new theoretical framework for prescribed-time stability using integral and calculus techniques, applicable to directed, disconnected, and multiweighted networks.

Findings

Prescribed-time synchronization achieved regardless of initial states.

The method handles directed, asymmetric, and disconnected network topologies.

Simulations confirm the effectiveness of the proposed approach.

Abstract

In this note, we study the prescribed-time (PT) synchronization of multiweighted and directed complex networks (MWDCNs) via pinning control. Unlike finite-time and fixed-time synchronization, the time for synchronization can be preset as needed, which is independent of initial values and parameters like coupling strength. First and foremost, we reveal the essence of PT stability by improper integral, L'Hospital rule and Taylor expansion theory. Many controllers established previously for PT stability can be included in our new model. Then, we apply this new result on MWDCNs as an application. The synchronization error at the prescribed time is discussed carefully, so, PT synchronization can be reached. The network topology can be directed and disconnected, which means that the outer coupling matrices (OCMs) can be asymmetric and not connected. The relationships between nodes are allowed to be cooperative or competitive, so elements in OCMs and inner coupling matrices (ICMs) can be positive or negative. We use the rearranging variables' order technique to combine ICMs and OCMs together to get the sum matrices, which can make a bridge between multiweighted and single-weighted networks. Finally, simulations are presented to illustrate the effectiveness of our theory.