分数阶线性退化微分系统有限时间镇定性问题  

Finite-time Stabilizability of Fractional Linear Singular Differential System

作　　者：王盼盼 张志信[1] 蒋威[1] WANG Panpan;ZHANG Zhixin;JIANG Wei(School of Mathematical Sciences,Anhui University,Hefei 230601)

机构地区：[1]安徽大学数学科学学院

出　　处：《应用数学学报》2020年第1期99-107,共9页Acta Mathematicae Applicatae Sinica

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)资助项目

摘　　要：本文通过构造新的Lyapunov函数,利用线性矩阵不等式(LMI)和广义Gronwall不等式,研究了分数阶线性退化微分系统的有限时间镇定性问题.充分考虑退化和扰动对系统稳定性的影响,给出了在状态反馈控制器作用下,分数阶退化微分系统在有限时间内镇定的充分条件.并通过两个例子验证了定理条件的可行性.In this paper,by constructing a new Lyapunov function,using linear matrix inequality(LMI) and generalized Gronwall inequality,the finite-time stabilizability of fractional-order linear singular differential system is studied.Considering the influence of singular and disturbance on the stabilizability of the system,some sufficient conditions under a state feedback which makes the fractional linear singular differential system stable in finite time are derived.Two examples are given to check the feasibility of the conditions of the theorems.

关 键 词：分数阶 退化 LYAPUNOV函数 有限时间镇定 线性矩阵不等式 

分 类 号：O175.15[理学—数学]