分数阶线性时滞微分系统的有限时间稳定性  

Finite-Time Stability of Fractional-Order Linear Differential Systems With Delays

作　　者：田洪乔 张志信[1] 蒋威[1] TIAN Hongqiao;ZHANG Zhixin;JIANG Wei(School of Mathematical Sciences,Anhui University,Hefei 230601,P.R.China)

机构地区：[1]安徽大学数学科学学院,合肥230601

出　　处：《应用数学和力学》2020年第8期921-930,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11471015;61272530;11371027);安徽省自然科学基金(1608085MA12;2008085QA19)。

摘　　要：该文研究了含有时滞的分数阶微分系统的有限时间稳定性问题.首先通过构造新的Lyapunov函数,利用线性矩阵不等式给出线性分数阶时滞微分系统的有限时间稳定性条件.其次,在状态反馈控制器的作用下,给出分数阶时滞微分闭环系统的有限时间稳定条件,同时给出了控制器的设计方法.最后,通过两个例子来说明所得理论结果的有效性.The finite-time stability of fractional-order linear differential systems with time delays was studied.Firstly,with a new Lyapunov function and the linear matrix inequality,some sufficient conditions for the finite-time stability of fractional linear differential systems with time delays were derived.Then,under the action of a state feedback controller,some conditions for the finite-time stability of fractional differential closed-loop systems with time delays were given,and the design method for the controller was given.In the end,the effectiveness of the theoretical results was illustrated with two examples.

关 键 词：分数阶 时滞 有限时间稳定 LYAPUNOV函数 线性矩阵不等式 

分 类 号：O175.15[理学—数学]