分数阶线性系统稳定理论在混沌同步中的简便应用  

Stability Theorem for Tractional Linear Systems and Its Application in Chaos Synchronization

作　　者：郝建红[1] 宾虹 姜苏娜 张潇 

机构地区：[1]华北电力大学电气与电子工程学院,北京102206

出　　处：《河北师范大学学报（自然科学版）》2014年第5期469-475,共7页Journal of Hebei Normal University：Natural Science

基　　金：国家自然科学基金(61372050);科技部国际科技合作项目(2011DFR00780)

摘　　要：针对分数阶混沌同步问题,基于矩阵理论,实现了分数阶线性系统稳定理论在同步控制器设计中的简便应用.所提方法放弃了原有设计中线性系统系数矩阵特征值的求解,利用矩阵性质完成控制器的设计,减少了计算量.以分数阶Lorenz混沌系统和分数阶耦合发电机混沌系统的投影同步,及分数阶超混沌Chen系统和分数阶超混沌Rssler系统的完全同步为研究对象,数值仿真验证了所提方法的有效性及可行性.For synchronization problem of fractional chaotic systems, based on matrix theory, stability theory of fractional linear systems was simply applied in the controller design. The proposed method utilizes the properties of linear system＇s coefficient matrix instead of calculating of matrix＇s eigenvalues to design the controller, which greatly reduce the calculations amount. Taking the projective synchronization between fractional Lorenz chaotic system and fractional coupled dynamos chaotic system, as well as the complete synchronization between fractional hyperchaotic Chen system and fractional hyperchaotic Rossler system for example, numerical simulation certifies the effectiveness and the feasibility of the proposed method.

关 键 词：分数阶线性系统 混沌 同步 稳定性 

分 类 号：O415.5[理学—理论物理]