一类非线性系统的非周期间歇H∞同步

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。%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.