分数阶退化时滞微分系统的有限时间镇定性问题  

Finite-Time Stabilization of Fractional Order Singular Differential Systems with Delay

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)

机构地区：[1]安徽大学数学科学学院,合肥230601

出　　处：《系统科学与数学》2021年第11期3000-3007,共8页Journal of Systems Science and Mathematical Sciences

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

摘　　要：文章研究了带有扰动的分数阶线性退化时滞微分系统的有限时间镇定性问题.通过构造新的Lyapunov函数和利用线性矩阵不等式(LMI),以及广义Gronwall不等式的方法,研究了退化、时滞和扰动对系统有限时间稳定性的影响,并且在反馈控制器作用下,得到了系统在有限时间内镇定的条件.最后,给出具体数值例子和系统模拟验证了文章定理条件的合理性和结论的正确性.In this paper,the finite time stabilization of fractional-order linear singular delay differential systems is studied.By constructing a new Lyapunov function and using the linear matrix inequality(LMI),as well as the generalized Gronwall inequality,we study the effects of singular,delay,and perturbations on the finite time stability of the systems.Under the action of the feedback controller,the condition of stabilization in finite time is obtained.Finally,a numerical example and system simulation are given to verify the rationality of the theorem conditions and the correctness of the conclusion.

关 键 词：分数阶 退化 时滞 LYAPUNOV函数 有限时间镇定 

分 类 号：O175[理学—数学] O231[理学—基础数学]