随机Lur’e时滞网络的指数同步与脉冲控制

Exponential synchronization and impulsive control of stochastic Lur’e delayed networks

本文研究了一类具有不对称耦合和时变时滞随机Lur’e动态网络的全局指数同步问题.为了使网络中的所有Lur’e系统达到同步,文章提出了一种实用的脉冲控制策略,利用平均脉冲间隔概念、Perron-Frobenius定理、比较原理、参数变分法和无参照系统策略,给出了保证网络实现全局指数同步的充分条件.基于脉冲信号既能促进网络群聚行为同时也可能阻碍网络同步这一事实,本文分别讨论了积极脉冲效应和消极脉冲效应作用下网络实现同步的判定方法,同时给出了不同脉冲效应作用下网络的收敛速度.提供了数值仿真证明主要结果和控制策略的有效性.

In this paper,we study the global and exponential synchronization problem for a class of stochastic Lur’e dynamical networks with asymmetric coupling and time-varying delays.Using the concept of average impulsive interval,the Perron-Frobenius theorem,the comparison principle,the parameter variation method and the target-free strategy,the sufficient conditions to ensure the global and exponential synchronization of the networks are given.Based on the fact that impulsive signals can promote network clustering behavior and may hinder network synchronization,this paper discusses the determination methods for network synchronization under the action of positive impulsive effects and negative impulsive effects,and gives the convergence speed under different impulsive effects.Numerical simulations are provided to demonstrate the main results and the effectiveness of the control strategy.