Caputo分数阶切换线性系统的指数稳定性  

Exponential stability of Caputo fractional order switched linear system

作　　者：王其祥 龙飞[2,3] 莫立坡 杨靖 WANG Qi-xiang;LONG Fei;MO Li-po;YANG Jing(School of Electrical Engineering,Guizhou University,Guiyang Guizhou 550025,China;School of Artificial Intelligence and Electrical Engineering,Guizhou Institute of technology,Guiyang Guizhou 550003,China;Guizhou Key Laboratory of Artificial Intelligence and Intelligent Control,Guiyang Guizhou 550003,China;School of Mathematics and Statistics,Beijing Industrial and Commercial University,Beijing 100048,China)

机构地区：[1]贵州大学电气工程学院,贵州贵阳550025 [2]贵州理工学院人工智能与电气工程学院,贵州贵阳550003 [3]贵州省人工智能与智能控制特色重点实验室,贵州贵阳550003 [4]北京工商大学数学与统计学院,北京100048

出　　处：《控制理论与应用》2023年第2期304-312,共9页Control Theory & Applications

基　　金：国家自然科学基金项目(61813006,61973329);贵州省基础研究计划重点项目(20191416);贵州省教育厅创新群体(黔教合KY字[2021]012);贵州省科技基金(黔科合基础[2020]1Y266);贵州省工业攻关项目(黔科合支撑[2019]2152);物联网理论与应用案例库(KCALK201708)资助。

摘　　要：众所周知,与整数阶切换系统不同, Caputo分数阶切换系统的积分下界不能随子系统的切换而被更新,意味着在下界非一致的任意区间内不能直接取分数阶导数的分数阶积分.对此,本文给出了一个不等式(文中引理6)克服这一问题,并用1个数值例子进行了验证.通过这一不等式,然后分别利用多Lyapunov函数方法和模型依赖平均驻留时间(MDADT)方法,给出了Caputo分数阶切换线性系统指数稳定的条件,并利用2个数值例子进行验证.As we all know,different from the integer order switched systems,the integral lower bound of Caputo fractional order switched systems cannot be updated with the switching of subsystems,which means that the fractional integral of fractional derivative cannot be taken directly in any interval with non-uniform lower bound.In order to overcome the above problem,an inequality(Lemma 6)is given in this paper.Through this inequality,the sufficient condition for the exponential stability of Caputo fractional order switched linear systems is given by using the multiple Lyapunov function and the model-dependent average dwell time(MDADT)method,respectively.Finally,two number examples are provided to verify the results.

关 键 词：Caputo分数阶切换线性系统 多LYAPUNOV函数 模型依赖平均驻留时间 指数稳定性 

分 类 号：O172[理学—数学]