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分数阶线性时滞微分系统的有限时间稳定性

田洪乔 张志信 蒋威

田洪乔, 张志信, 蒋威. 分数阶线性时滞微分系统的有限时间稳定性[J]. 应用数学和力学, 2020, 41(8): 921-930. doi: 10.21656/1000-0887.400365
引用本文: 田洪乔, 张志信, 蒋威. 分数阶线性时滞微分系统的有限时间稳定性[J]. 应用数学和力学, 2020, 41(8): 921-930. doi: 10.21656/1000-0887.400365
TIAN Hongqiao, ZHANG Zhixin, JIANG Wei. Finite-Time Stability of Fractional-Oder Linear Differential Systems With Delays[J]. Applied Mathematics and Mechanics, 2020, 41(8): 921-930. doi: 10.21656/1000-0887.400365
Citation: TIAN Hongqiao, ZHANG Zhixin, JIANG Wei. Finite-Time Stability of Fractional-Oder Linear Differential Systems With Delays[J]. Applied Mathematics and Mechanics, 2020, 41(8): 921-930. doi: 10.21656/1000-0887.400365

分数阶线性时滞微分系统的有限时间稳定性

doi: 10.21656/1000-0887.400365
基金项目: 国家自然科学基金(11471015;61272530;11371027);安徽省自然科学基金(1608085MA12;2008085QA19)
详细信息
    作者简介:

    田洪乔(1995—),女,硕士生(E-mail: 784043860@qq.com);张志信(1976—),男,副教授,硕士生导师(通讯作者. E-mail: zhang_zhi_x@sina.com);蒋威(1959—),男,教授,博士生导师(E-mail: jiangwei@ahu.edu.cn).

  • 中图分类号: O175.15

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

Funds: The National Natural Science Foundation of China(11471015;61272530;11371027)
  • 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.
  • [1] KILBAS A A, SRIVASTAVA H M, TRUJILLO J J. Theory and Applications of Fractional Differential Equations [M]. New York: Elsevier, 2006.
    [2] PODLUBNY I. Fractional Differential Equations [M]. San Diego: Academic Press, 1999.
    [3] DUARTE-MERMOUD M A, AGUILA-CAMACHO N, GALLEGOS J A. Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems[J]. Communications in Nonlinear Science and Numerical Simulation,2015,22(1/3): 650-659.
    [4] MA Y J, WU B W, WANG Y E. Finite-time stability and finite-time boundedness of fractional order linear systems[J]. Neurocomputing,2016,173(3): 2076-2082.
    [5] 王利敏, 宋乾坤, 赵振江. 基于忆阻的分数阶时滞复值神经网络的全局渐近稳定性[J]. 应用数学和力学, 2017,38(3): 333-346.(WANG Limin, SONG Qiankun, ZHAO Zhenjiang. Global asymptotic stability of memristor-based fractional-order complex-valued neural networks with time delays[J]. Applied Mathematics and Mechanics,2017,38(3): 333-346.(in Chinese))
    [6] 张平奎, 杨绪君. 基于激励滑模控制的分数阶神经网络的修正投影同步研究[J]. 应用数学和力学, 2018,39(3): 343-354.(ZHANG Pingkui, YANG Xujun. Modified projective synchronization of a class of fractional-order neural networks based on active sliding mode control[J]. Applied Mathematics and Mechanics,2018,39(3): 343-354.(in Chinese))
    [7] AMATO F, ARIOLA M, DORATO P. Finite-time control of linear systems subject to parametric uncertainties and disturbances[J]. Automatica,2001,37(9): 1459-1463.
    [8] LAZAREVICM P, SPASICA M. Finite-time stability analysis of fractional order time-delay systems: Gronwall’s approach[J]. Mathematical and Computer Modelling,2009,49(3/4): 475-481.
    [9] ZHANG X Y. Some results of linear fractional order time-delay system[J]. Applied Mathematics and Computation,2008,197(1): 407-411.
    [10] LAZAREVIC M P. Further results on finite time partial stability of fractional order time delay systems[C]//6th Workshop on Fractional Differentiation and Its Applications Part of 2013 IFAC Joint Conference SSSC . Grenoble, France, 2013.
    [11] HEI X D, WU R C. Finite-time stability of impulsive fractional-order systems with time-delay[J]. Applied Mathematical Modelling,2016,40(7/8): 4285-4290.
    [12] PHAT V N, THANH N T. New criteria for finite-time stability of nonlinear fractional-order delay systems: a Gronwall inequality approach[J]. Applied Mathematics Letters,2018,83: 169-175.
    [13] LI M M, WANG J R. Finite time stability of fractional delay differential equations[J]. Applied Mathematics Letters,2017,64: 170-176.
    [14] LI M M, WANG J R. Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations[J]. Applied Mathematics and Computation,2018,324: 254-265.
    [15] YANG X J, SONG Q K, LIU Y R. Finite-time stability analysis of fractional-order neural networks with delay[J]. Neurocomputing,2015,152: 19-26.
    [16] WU R C, LU Y F, CHEN L P. Finite-time stability of fractional delayed neural networks[J]. Neurocomputing,2015,149(B): 700-707.
    [17] SHEN J, LAM J. Non-existence of finite-time stable equilibria in fractional-order nonlinear systems[J]. Automatica,2014,50: 547-551.
    [18] MUNOZ-V AZQUEZ A J, ANAND S O, PARRA-VEGA V. A general result on non-existence of finite-time stable equilibria in fractional-order systems[J]. Journal of the Franklin Institute,2019,356: 268-275.
    [19] ZHENG M W, XIAO J H, ZHAO H. Finite-time stability and synchronization of memristor-based fractional-order fuzzy cellular neural networks[J]. Communications in Nonlinear Science and Numerical Simulation,2018,59: 272-291.
    [20] PAN B F, FAREED U, QING W J, et al. A novel fractional order PID navigation guidance law by finite time stability approach[J]. ISA Transactions,2019,94: 80-92.
    [21] LIU S, ZHOU X F, LI X Y, et al. Asymptotical stability of Riemann-Liouville fractional singular systems with multiple time-varying delays[J]. Applied Mathematics Letters,2017,65: 32-39.
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出版历程
  • 收稿日期:  2019-12-03
  • 修回日期:  2020-06-20
  • 刊出日期:  2020-08-01

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