分数阶时滞统一混沌系统反馈控制器设计及稳定性分析  

Feedback controller design of fractional order unified chaotic system with time delay and its stability analysis

作　　者：陈志旺[1] 张健[1] 赵子铮 张子振[1] 邵玉杰[1] CHEN Zhiwang ZHANG Jian ZHAO Zizheng ZHANG Zizhen SHAO Yujie(School of Electrical Engineering , Yanshan University , Qinhuangdao , Hebei 066004, Chin)

机构地区：[1]燕山大学电气工程学院,河北秦皇岛066004

出　　处：《燕山大学学报》2017年第2期156-163,共8页Journal of Yanshan University

基　　金：国家自然科学基金资助项目(61573305;61403332)

摘　　要：本文针对分数阶时滞统一混沌系统设计了一种时滞相关的反馈控制器。首先通过响应-驱动同步法求得两混沌系统的误差系统,根据误差系统设计了由非时滞误差项和时滞误差项组成的状态反馈控制器。然后,针对带有控制器的误差系统,利用Nyquist稳定判据证明了它线性部分的稳定性。在此基础上又利用Lyapunov函数法对整个误差控制系统的稳定性进行了证明。最后仿真验证了控制器的有效性,并得出反馈系数对系统暂态性能影响的规律。In this paper, a kind of delay-dependent feedback controller is designed for fractional order unified chaotic system with time delay.Firstly , the error system is obtained by calculating the difference between the response system and driving system in the drive-response method.And the controller is designed according to the error item and error item w-ith time delay in error system. Secondly , the stability of the linear part of the error system with the controller is proved by Nyquist stability criterion. On the basis of the linear part stability , the stability of the whole error control system is proved by the Lyapunov function method.Finally , numerical simulations are presented to verify the effectiveness of the method , and obtain the rule about the effects of feedback coefficient on transient performance of the system.

关 键 词：混沌同步 分数阶统一混沌系统 时滞系统 稳定性分析 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]