具有Caputo导数的分数阶退化脉冲微分系统的有限时间稳定性  

Finite-Time Stability of Fractional-Order Singular Impulsive Systems with Caputo Derivative

作　　者：吴桐 张志信[1] 蒋威[1] WU Tong;ZHANG Zhixing;JIANG Wei(School of Mathematical Sciences,Anhui University,Hefei 230601,China)

机构地区：[1]安徽大学数学科学学院

出　　处：《应用数学》2020年第1期202-208,共7页Mathematica Applicata

基　　金：国家自然科学基金(11371027,11471015,11601003);安徽省自然科学基金(1608085MA12);高等学校博士点专项科研资助基金(20123401120001)

摘　　要：本文通过构建新的Lyapunov泛函,并利用Caputo导数的相关性质以及广义的Gronwall不等式研究了同时带有扰动和脉冲因素的分数阶退化线性系统在Caputo导数意义下的有限时间稳定性问题.在此基础上给出了在没有扰动的情形下分数阶退化脉冲微分系统的有限时间稳定性的判据,所获得的结果推广了相关文献的结论.最后针对不同的情况给出具体数值例子验证了定理条件的有效性.Finite-time stability problem of fractional order linear singular systems in the sense of Caputo with both disturbance and impulse factors is studied in this paper by constructing a new Lyapunov functional,using the related properties for Caputo fractional derivative and the generalized Gronwall inequality.On this basis,the finite-time stability criterion of fractional order singular impulsive differential system without disturbance was given.The results obtained extend the conclusions of the relevant literatures.Finally,some numerical examples are given for different cases to verify the validity of the theorem conditions.

关 键 词：分数阶 CAPUTO导数 退化 脉冲 有限时间稳定性 

分 类 号：O175.13[理学—数学]