Caputo分数阶延迟微分系统的渐近稳定性The Asymptotic Ctability of Caputo Fractional Order Delay Differential Equations
潘新元;
摘要(Abstract):
本文给出了Caputo分数阶线性延迟微分系统真解渐近稳定的充分条件,并进行了严格证明。
关键词(KeyWords): Caputo分数阶层数;分数阶线性延迟微分方程;渐近稳定性;数值方法
基金项目(Foundation):
作者(Authors): 潘新元;
DOI: 10.16778/j.cnki.1671-5934.2011.06.003
参考文献(References):
- [1]PODLUBNG I.Fractional dierential equations[M].SanDiego:Academic Press,1999.
- [2]LUBICH C.Discretized fractional calculus[J].SIAM J Math Anal,1986,17(3):704-716.
- [3]DIETHELM K.An algorithm for the numerical solution of dierential equations of fractional order[J].Elec.Trans.Numerical Al-gorithms,1997(16):231-253.
- [4]FORD N J,SIMPSON C.The numerical solution of fractional dierential equations:speed versus accuracy[J].Numerical Algo-rithms,2001(26):333-346.
- [5]FORD N J,SIMPSON C.Numerical approaches to the solution of some fractional dierential equations[J].Proceedings of Hercma,2001(5):100-107.
- [6]DIETHELM K,FORD N,FREED A D.A predictor-corrector approach for the numerical solutions of fractional dierential equa-tions[J].Nonlinear Dynamics,2002(29):3-22.
- [7]DIETHELM K,FORD N J,FREED A D.Detailed error analysis for a fractional Adams method[J].Numerical Algorithms,2004(36):31-52.
- [8]张秀云,寇春海.分数阶泛涵微分方程解的存在唯一性[J].东华大学学报:自然科学版,2007,33(4).
- [9]ZHANG Xiuyun.Some results of linear fractional order time-delay system[J].Applied Mathematics and Computation,2008(197):407-411.
- [10]CHEN Y Q,MOORE K L.Analytical stability bound for a class of delayed fractional-order dynamic systems[J].NonlinearDynamics,2002,29(1):191-200.
- [11]HWANGA C,YI Chengcheng,A numerical algorithm for stability testing of fractional delay systems with multiple time delays[J].Automatica,2006(42):825-831.
- [12]LAKSHMIKANTHAM V.Theory of fractional functional dierential equations[J].Nonlinear Analysis,2007(9):25
- [13]HENDERSON J,OUAHAB A.Fractional functional dierential inclusions with nite delay[J].Nonlinear Analysis,2008(2):111.
- [14]DENG W,LI Changpin,LU Jinhu.Stability analysis of linear fractional dierential system[J],Nonlinear Dyn,2007(48):409-416.
- [15]GALEONE L,GARRAPPA R.On multistep methods for dierential equations of fractional Or-der[J],Mediterr J Math,2006(3):565-580.
- [16]郑君里.信号与系统[M].第2版,北京:高等教育出版社,2010.
- [17]匡蛟勋.泛涵微分方程的数值处理[M].北京:科学出版社,1999.