具有时变时滞的非线性分数阶退化微分系统的有限时间稳定性  

Finite-time Stability of Nonlinear Fractional Singular Systems with Time-varying Delay

作　　者：吴桐 张志信[1] 蒋威[1] WU TONG;ZHANG ZHIXIN;JIANG WEI(School of Mathematical Sciences,AnhuiUniversity,Hefei 230601,China)

机构地区：[1]安徽大学数学科学学院,合肥230601

出　　处：《应用数学学报》2023年第1期32-44,共13页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(No.11371027,11471015,11601003);安徽省自然科学基金(No.2008085QA19)资助项目。

摘　　要：本文研究了一类具有时变时滞的非线性分数阶退化微分系统的有限时间稳定性问题.首先通过退化微分系统理论得到了系统正则无脉冲的充分性条件.在此基础上通过建立Lyapunov泛函,并利用广义Gronwall不等式和线性矩阵不等式方法给出了含有时变时滞因素的分数阶退化微分系统的有限时间稳定性判据.最后给出具体的算例验证了定理条件的有效性.Finite-time stability problem of nonlinear fractional singular system with time-varying delay is studied in this paper.First,the sufficient conditions for the systems to be regular and impulse-free are obtained by using singular system theory.On this basis,by constructing Lyapunov function,the finite-time stability criterions for fractional singular differential system with time-varying delay factor are derived via the generalized Gronwall inequality and linear matrix inequality method.Finally,a numerical examples is given to verify the validity of the theorem conditions.

关 键 词：分数阶 退化 非线性 时变时滞 有限时间稳定 

分 类 号：O175.13[理学—数学]