广义分数阶混沌系统的鲁棒同步研究  

Robust Synchronization of Singular Fractional Order Chaotic Systems

作　　者：刘焕霞 赵鑫 林崇[1] 马瑞兰[1] LIU Huanxia;ZHAO Nin;LIN Chong;MA Ruilan(Institute of Complexity Science,Qingdao University,Qingdao 266071,China)

机构地区：[1]青岛大学复杂性科学研究所,山东青岛266071

出　　处：《青岛大学学报（工程技术版）》2018年第2期21-25,共5页Journal of Qingdao University(Engineering & Technology Edition)

基　　金：国家自然科学基金资助项目(61673227)

摘　　要：针对广义分数阶混沌系统在微分阶数0<α<1时的鲁棒同步问题,本文通过构造同步信号得到响应系统,利用实数域上正常广义分数阶系统的可容许性判据,结合Schur Complement定理等,进一步考虑广义分数阶不确定混沌系统的鲁棒同步问题。经过理论推导,以线性矩阵不等式的形式给出一种广义分数阶不确定混沌系统鲁棒同步的充分必要条件,并求出状态反馈控制率,并利用两个数值例子进行证明。结果表明,与已有分数阶混沌系统鲁棒同步定理相比,本文所得结果变量较少,结果以及推导过程简洁,对于正则性未知的广义分数阶混沌系统同样适用,适用范围较广,说明了本研究的有效性。该研究为广义分数阶不确定混沌系统的鲁棒同步问题提供了理论指导。This paper studies generalized fractional order chaotic systems under differential order 0〈α〈1 is studied.The response system is obtained by constructing the synchronization signals.By using a new criterion for admissibility of singular fractional order systems in real numbers and Schur Complement theorem,it further studies the synchronous robustness problem of singular fractional order chaotic systems.After rigorous theoretical derivation,a necessary and sufficient condition for the robust synchronization of generalized fractional order uncertain chaotic systems is given in the form of linear matrix inequalities（LMIs）,and the state feedback control rate is obtained,and two numerical examples are used to verify the method.The results show that compared with the existing robust synchronization theorem of fractional-order chaotic system,the results obtained in this paper contain less variables and the derivation process is succinct.The generalized fractional-order chaotic system with unknown regularity is also applicable,and the scope of application is wide,which shows the effectiveness of this study.It provides theoretical guidance for the robust synchronization problem of generalized fractional-order uncertain chaotic systems.

关 键 词：分数阶混沌系统 广义系统 不确定性 鲁棒同步 可容许 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程] O231.1[自动化与计算机技术—控制科学与工程]