Mathematics

CLC number: TP13

Modified Fixed-Time Synchronization Criteria of Complex Networks with Time-Varying Delays via Continuous or Discontinuous Control

基于连续或不连续控制的时变时滞复杂网络的修正固定时间同步判据

School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, Hubei, China

^† Corresponding author. E-mail: hbnuwu@yeah.net

Received: 10 February 2024

Abstract

This paper investigates modified fixed-time synchronization (FxTS) of complex networks (CNs) with time-varying delays based on continuous and discontinuous controllers. First, for the sake of making the settling time (ST) of FxTS is independent of the initial values and parameters of the CNs, a modified fixed-time (FxT) stability theorem is proposed, where the ST is determined by an arbitrary positive number given in advance. Then, continuous controller and discontinuous controller are designed to realize the modified FxTS target of CNs. In addition, based on the designed controllers, CNs can achieve synchronization at any given time, or even earlier. And control strategies effectively solve the problem of ST related to the parameters of CNs. Finally, an appropriate simulation example is conducted to examine the effectiveness of the designed control strategies.

摘要

本文基于连续和不连续控制器，研究了带有时变时滞的复杂网络的修正固定时间同步。首先，为了保证固定时间同步的确定时间与复杂网络的初始值和参数都无关，提出了一个修正的固定时间稳定性定理，其中确定时间是由提前给定的任意正数决定。然后，设计了连续控制器和不连续控制器，用于实现复杂网络的固定时间同步目标。基于所设计的控制器，复杂网络可以在任意给定时间甚至更早实现同步。并且控制策略有效解决了确定时间与复杂网络参数有关的问题。最后通过仿真实例验证了所设计控制策略的有效性。