Caputo-Fabrizio分数阶线性动力系统的可观测性和可控制性  

Observability and Controllability of Caputo-Fabrizio Fractional Linear Dynamical Systems

作　　者：赵正祥 李晓艳[1] 刘松[1] ZHAO Zheng-xiang;LI Xiao-yan;LIU Song(School of Mathematical Science,Anhui University,Hefei 230601,China)

机构地区：[1]安徽大学数学科学学院,合肥230601

出　　处：《合肥学院学报（综合版）》2020年第2期14-18,共5页Journal of Hefei University：Comprehensive ED

基　　金：安徽省自然科学重点项目(KJ2019A0004)资助。

摘　　要：针对Caputo-Fabrizio分数阶线性动力系统的可观测性和可控制性进行了研究。首先利用Caputo-Fabrizio分数阶导数及单位脉冲函数的Laplace变换得到了方程解的表达式,进而得到可控制性和可观测性的Grammian矩阵,由此给出并证明了可观测性和可控制性的充分必要条件。This paper mainly studies the observability and controllability of Caputo-Fabrizio fractional linear dynamic system.Firstly,the expression of the equation solution is obtained by using the Laplace transform of the Caputo-Fabrizio fractional derivative and the unit impulse function,and then the Grammian matrix of controllability and observability is acquired.At last,the necessary and sufficient conditions for controllability and observability are given respectively.

关 键 词：Grammian矩阵 Caputo-Fabrizio分数阶微分 LAPLACE变换 可控制性 可观测性 

分 类 号：O175.14[理学—数学]