一类非线性系统的非周期间歇H∞同步

Aperiodically Intermittent H∞ Synchronization for a Class of Nonlinear System

关键词:  非线性系统  切换Lyapunov函数  H_∞同步  间歇控制

Key words:  nonlinear systems  switching Lyapunov function  H_∞ synchronization  intermittent control

摘要:

基于H_∞控制理论研究一类非线性系统的间歇H_∞同步问题.针对间歇控制具有切换控制的特征,通过构造时变切换的Lyapunov函数并结合凸组合技术,分析误差系统的稳定性和L₂-增益性能;基于线性矩阵不等式技术,设计非周期间歇H_∞同步控制器;用数值例子验证所提出方法的有效性.与以往结果相比,本文提出的间歇控制窗口宽度和休息窗口宽度是可变的,即非周期间歇控制,而且新提出的Lyapunov函数在闭环和开环模式上都是非增的,保证同步误差系统是内指数稳定并且具有规定L₂-增益.

Abstract:

The external disturbances are inevitable in the synchronization process.In this paper, the H_∞ synchronization problem for a class of nonlinear system is investigated via intermittent control based on the H_∞ control theory.Different from the previous results,the control and rest window width are variable in this paper,that is aperiodically intermittent control.Owing to the switching characteristics of intermittent control,a switching-time-various Lyapunov function combined with the convex combination technique is applied to analyze the stability and L₂-gain performance of error system.It is worth mentioning that the Lyapunov function proposed in this paper is non-increasing in the closed-model and open-model.By linear matrix inequality technique,the aperiodically intermittent H_∞ synchronization feedback controller is presented,which can ensure the internally exponential stability and have a prescribed L₂-gain.Finally,a numerical example demonstrates the effectiveness of the obtained results.