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分数阶时滞系统的稳定性 被引量：2

Stability of fractional differential system with time delays
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摘要 文章讨论了分数阶线性系统的稳定性问题,其中一部分状态含有时滞。借助Laplace变换,引入时滞系统的特征方程,最后,利用特征方程的根全部具有负实部则系统稳定的性质对系统稳定性进行了分析。 This article mainly discusses stability of fractional differential system some of which the state contains time delays.With the Laplace transformation,we introduces time delays system characteristic equation,and we all know that the system is stable if all roots of the characteristic equation have negative parts.At last,we study the stability of this system by using the result.
作者 方园
机构地区 阜阳师范学院数学与计算科学学院
出处 《阜阳师范学院学报（自然科学版）》 2012年第3期11-13,共3页 Journal of Fuyang Normal University(Natural Science)
基金 教育部 财政部第四批高等学校特色专业建设点(TS11496)资助
关键词 分数阶 时滞 LAPLACE变换 稳定 fractional delay Laplace transformation stability
分类号 O231.1 [理学—运筹学与控制论]
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参考文献6

  • 1Deng W H, Li C P, Ltl J H. Stability analysis of linear fractional differential system with multiple time delays [ J ]. Nonlinear Dynamics,2007,48:409-416.
  • 2Qian D L,Li C P,Agarwal R P,et al. Stability analysis of fractional differential system with Riemann-Liouville derivative [ J ]. Mathematical and Computer Modelling, 2010,52 : 862-874.
  • 3Ahn H S, Chen Y Q. Necessary and sufficient stability condition of fractional-order interval linear systems [ J ]. Automatica, 2008,44 : 2985-2988.
  • 4Li Y, Chen, Igor P Y Q. Stability of fractional-order non- linear dynamic systems: Lyapunov direct method and generalized Mittag-Leitler stability [ J ]. Computers and Mathematics with Applications, 2010,59:1810-1821.
  • 5Xing S Y, Lu J G. Robust stability and stabilization of fractional-order linear systems with nonlinear uncertain parameters : An LMI approach [ J ]. Chaos, Solitons and Fractals ,2009,42 : 1163-1169.
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同被引文献13

  • 1Vijayakumar V, Selvakumar A, Murugesu R. Controllability for a Class of Fractional Neutral Integro - differential Equa- tions with Unbounded Delay[J]. Applied Mathematics and Computation, 2014,232 : 303 - 312.
  • 2Aguila - Camacho N 1. Lyapunov Functions for Fractional Order Systems [ EB/OL]//Commun Nonlinear Sci Numer Simulat (2014), http ://dx. doi, org/10. 1016/j. cnsns. 2014 -01 -22.
  • 3Ivanka Stamova, Gani Stamov. Stability Analysis of Impul- sive Functional Systems of Fractional Order [ J ]. Commun Nonlinear Sci Numer Simulat ,2014,19:702 - 709.
  • 4Li Yan, Chen Yangquan, Igor Podlubny. Stability of Frac- tional - order Nonlinear Dynamic Systems : Lyapunov Direct Method and Generalized Mittag - Leffler Stability [ J ]. Com- puters and Mathematics with Applications, 2010,59 : 1810 - 1821.
  • 5Yuan FANG. State Feedback Control for Fractional Differ- ential Systems with Riemann - Liouville Derivative [ C ]// Materials Engineering and Automatic Control. Switzerland: Trans Tech Publications Ltd,2012:2053 -2056.
  • 6Saeed Balochian, Ali Khaki Sedigh, Asef Zare. Stabilization of Multi - input Hybrid Fractional - order Systems with State Delay[ J]. ISA Transactions,2011,50:21 - 27.
  • 7Hale J K. Theory of Functional Differential Equations [ M ]. New York : Springer - Verlag, 1977.
  • 8Yong-Hong Lan,Yong Zhou.LMI-based robust control of fractional-order uncertain linear systems[J]. Computers and Mathematics with Applications . 2011 (3)
  • 9Deliang Qian,Changpin Li,Ravi P. Agarwal,Patricia J.Y. Wong.Stability analysis of fractional differential system with Riemann–Liouville derivative[J]. Mathematical and Computer Modelling . 2010 (5)
  • 10Chilali, M.,Gahinet, P.,Apkarian, P.Robust pole placement in LMI regions. Automatic Control, IEEE Transactions on . 1999

引证文献2

阜阳师范学院学报（自然科学版）
2012年 第3期

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