含脉冲分数阶广义线性系统的能控能观性  

On the controllability and observability of fractional singular linear system with impulses

作　　者：冯再勇 叶玲华[3] 向峥嵘[1] 谢小韦[2] FENG Zaiyong;YE Linghua;XIANG Zhengrong;XIE Xiaowei(School of Automation,Nanjing University of Science and Technology,Nanjing 210094,China;Department of Basic Sciences,Nanjing Institute of Railway Technology,Nanjing 210031,China;Department of Financial Office,Nanjing Institute of Railway Technology,Nanjing 210031,China)

机构地区：[1]南京理工大学自动化学院,江苏南京210094 [2]南京铁道职业技术学院基础部,江苏南京210031 [3]南京铁道职业技术学院财务处,江苏南京210031

出　　处：《南昌大学学报（理科版）》2021年第5期416-424,共9页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(61873128);江苏高校“青蓝工程”资助项目(2019、2021);江苏省轨道交通控制工程技术研究开发中心基金(KFJ2010);江苏省现代教育研究重点课题(2018-R-66273);江苏省高等学校自然科学研究面上项目(17KJB120008)。

摘　　要：基于含脉冲分数阶广义线性系统的状态响应,研究了含脉冲分数阶广义线性系统的完全能控性和能观性问题.本文首先利用受限等价变换,将含脉冲分数阶广义线性系统分解为慢子系统和快子系统两部分.然后,基于含脉冲分数阶广义线性系统的状态响应,研究并给出了快子系统完全能控和完全能观的充要条件,进一步建立快子系统的完全能控和能观判据.综合慢子系统和快子系统的能控性、能观性定理,得到含脉冲分数阶广义线性系统的完全能控、完全能观判定定理.最后,相关算例验证了本文所提出定理和判据的有效性.Based on the distributional solution of the fractional singular linear system,the paper discussed the controllability and observability of the Fractional Singular Linear System with Impulses(FSLSI).Firstly,the FSLSI is decomposed into low subsystem and fast subsystem under restricted equivalent transformation.Then conditions of controllability and observability are investigated for the fast subsystem on the basis of the distributional solution of FSLSI,relative criterions are put forward.Synthesis of the conditions of controllability and observability for slow subsystem and fast subsystem derives the theorems of controllability and observability for FSLSI.The correctness of the proposed theorems and criterions are verified by two examples in the end.

关 键 词：分数阶 广义线性系统 能控性 能观性 含脉冲 

分 类 号：O231[理学—运筹学与控制论] TP13[理学—数学]