Finite-time stability criteria for a class of fractional-order neural networks with delay
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  • 作者:Liping Chen ; Cong Liu ; Ranchao Wu ; Yigang He ; Yi Chai
  • 关键词:Finite ; time stability ; Fractional order ; Neural network ; Delayed systems
  • 刊名:Neural Computing & Applications
  • 出版年:2016
  • 出版时间:April 2016
  • 年:2016
  • 卷:27
  • 期:3
  • 页码:549-556
  • 全文大小:528 KB
  • 参考文献:1.Rakkiyappan R, Chandrasekar A, Lakshmanan S, Park J, Jung H (2013) Effects of leakage time-varying delays in Markovian jump neural networks with impulse control. Neurocomputing 121:365–378CrossRef
    2.Rakkiyappan R, Chandrasekar A, Lakshmanan S, Park J (2014) Exponential stability of Markovian jumping stochastic Cohen–Grossberg neural networks with mode-dependent probabilistic time-varying delays and impulses. Neurocomputing 131:265–277CrossRef
    3.Li T, Wang T, Song A, Fei S (2013) Combined convex technique on delay-dependent stability for delayed neural networks. IEEE Trans Neural Netw Learn Syst 24(9):1459–1466CrossRef
    4.Wang X, Li C, Huang T, Duan S (2014) Global exponential stability of a class of memristive neural networks with time-varying delays. Neural Comput Appl 24(7–8):1707–1715CrossRef
    5.Rakkiyappan R, Zhu Q, Chandrasekar A (2014) Stability of stochastic neural networks of neutral type with markovian jumping parameters: A delay fractioning approach. J Franklin Inst 351(3):1553–1570MathSciNet CrossRef
    6.Xiao M, Zheng W, Cao J (2013) Bifurcation and control in a neural network with small and large delays. Neural Netw 44:132–142CrossRef MATH
    7.Lundstrom B, Higgs M, Spain W, Fairhall A (2008) Fractional differentiation by neocortical pyramidal neurons. Nat Neurosci 11:1335–1342CrossRef
    8.Anastasio T (1994) The fractional-order dynamics of brainstem vestibulooculomotor neurons. Biol Cybern 72:69–79CrossRef
    9.Anastassiou G (2012) Fractional neural network approximation. Comput Math Appl 64(6):1655–1676MathSciNet CrossRef MATH
    10.Boroomand A, Menhaj M (2009) Fractional-order Hopfield neural networks. Lecture Notes in Computer Science 5506:883–890
    11.Arena P, Fortua L, Porto D (2000) Chaotic behavior in noninteger-order cellular neural networks. Phys Rev E 61:776–781CrossRef
    12.Liu L, Liu C, Liang D (2013) Hyperchaotic behavior in arbitrary-dimensional fractional-order quantum cellular neural network model. Int J Bifurc Chaos 23(3):1350044MathSciNet CrossRef MATH
    13.Kaslik E, Sivasundaram S (2012) Nonlinear dynamics and chaos in fractional-order neural networks. Neural Netw 32:245–256CrossRef MATH
    14.Huang X, Zhao Z, Wang Z, Li Y (2012) Chaos and hyperchaos in fractional-order cellular neural networks. Neurocomputing 94:13–21CrossRef
    15.Wu R, Hei X, Chen L (2013) Finite-time stability of fractional-order neural networks with delay. Commun Theor Phys 60(2):189–193MathSciNet CrossRef MATH
    16.Chen L, Chai Y, Wu R, Ma T, Zhai H (2013) Dynamic analysis of a class of fractional-order neural networks with delay. Neurocomputing 111:190–194CrossRef
    17.Alofi A, Cao J, Elaiw A, Al-Mazrooei A (2014) Delay-dependent stability criterion of Caputo fractional neural networks with distributed delay. Discret Dyn Nat Soc, 529358
    18.Chen L, Qu J, Chai Y, Wu R, Qi G (2013) Synchronization of a class of fractional-order chaotic neural networks. Entropy 15(8):3265–3276MathSciNet CrossRef
    19.Zhou S, Hua L, Zhua Z (2008) Chaos control and synchronization in a fractional neuron network system. Chaos Solitons Fractals 36(4):973–984MathSciNet CrossRef MATH
    20.Chen J, Zeng Z, Jiang P (2014) Global Mittag–Leffler stability and synchronization of memristor-based fractional-order neural networks. Neural Netw 51:1–8CrossRef MATH
    21.Dorato P (1961) Short time stability in linear time-varying systems. In: Proceedings of IRE international convention record part 4:83–87
    22.Zhang X (2008) Some results of linear fractional order time-delay system. Appl Math Comput 197:407–411MathSciNet MATH
    23.Lazarevic M, Spasic A (2009) Finite-time stability analysis of fractional order time-delay systems: Gronwall’s approach. Math Comput Model 49(3–4):475–481MathSciNet CrossRef MATH
    24.Lazarevic M, Debeljkovic D (2005) Finite time stability analysis of linear autonomous fractional order systems with delayed state. Asian J Control 7(4):440–447MathSciNet CrossRef
    25.Lazarevic M (2006) Finite time stability analysis of PD\(^\alpha \) fractional control of robotic time-delay systems. Mech Res Commun 33(2):269–279MathSciNet CrossRef MATH
    26.Aghababa M (2014) A Lyapunov-based control scheme for robust stabilization of fractional chaotic systems. Nonlinear Dyn 78:2129C2140MathSciNet CrossRef
    27.Roohi M, Aghababa M, Haghighi A (2014) Switching adaptive controllers to control fractional-order complex systems with unknown structure and input nonlinearities. Complexity. doi:10.​1002/​cplx.​21598
    28.Aghababa M (2014) Synchronization and stabilization of fractional second-order nonlinear complex systems. Nonlinear Dyn. doi:10.​1007/​s11071-014-1411-4
    29.Aghababa M (2014) Fractional modeling and control of a complex nonlinear energy supply-demand system. Complexity. doi:10.​1002/​cplx.​21533
    30.Haghighi A, Aghababa M, Roohi M (2014) Robust stabilization of a class of three-dimensional uncertain fractional-order non-autonomous systems. Int J Ind Math 6(2):133–139
    31.Aghababa M (2014) Control of fractional-order systems using chatter-free sliding mode approach. J Comput Nonlinear Dyn 9(3):031003CrossRef
    32.Aghababa M (2014) A switching fractional calculus-based controller for normal non-linear dynamical systems. Nonlinear Dyn 75(3):577–588MathSciNet CrossRef MATH
    33.Aghababa M (2014) Control of nonlinear non-integer-order systems using variable structure control theory. Trans Inst Measure Control 36(3):425–432CrossRef
    34.Aghababa M (2013) No-chatter variable structure control for fractional nonlinear complex systems. Nonlinear Dyn 73(4):2329–2342MathSciNet CrossRef MATH
    35.Aghababa M (2013) Design of a chatter-free terminal sliding mode controller for nonlinear fractional-order dynamical systems. Int J Control 86:1744–1756MathSciNet CrossRef MATH
    36.Aghababa M (2013) A novel terminal sliding mode controller for a class of non-autonomous fractional-order systems. Nonlinear Dyn 73(1–2):679–688MathSciNet CrossRef MATH
    37.Aghababa M (2012) Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic (hyperchaotic) systems using fractional nonsingular terminal sliding mode technique. Nonlinear Dyn 69(1–2):247–261MathSciNet CrossRef MATH
    38.Aghababa M (2012) Robust stabilization and synchronization of a class of fractional-order chaotic systems via a novel fractional sliding mode controller. Commun Nonlinear Sci Numer Simul 17:2670–2681MathSciNet CrossRef MATH
    39.Chen Y, Ahn H, Podlubny I (2007) Robust stability test of a class of linear time-invariant interval fractional-order system using Lyapunov inequality. Appl Math Comput 187(1):27–34MathSciNet MATH
    40.Moornani K, Mohammad H (2009) On robust stability of linear time invariant fractional-order systems with real parametric uncertainties. ISA Trans 48(4):484–490CrossRef
    41.Lim Y, Oh K, Ahn H (2013) Stability and stabilization of fractional-order linear systems subject to input saturation. IEEE Trans Autom Control 58(4):1062–1067MathSciNet CrossRef
    42.Deng W, Li C, Lu J (2007) Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dyn 48(4):409–416MathSciNet CrossRef MATH
    43.Sadati S, Baleanu D, Ranjbar A, Ghaderi R, Abdeljawad T (2010) Mittag–Leffler stability theorem for fractional nonlinear systems with delay. Abstr Appl Anal, 108651
    44.Li C, Deng W (2007) Remarks on fractional derivatives. Appl Math Comput 187(2):777–784MathSciNet MATH
    45.Mitrinovic D (1970) Analytic inequalities. Springer, BerlinCrossRef MATH
    46.Willett D (1964) Nonlinear vector integral equations as contraction mappings. Arch Ration Mech Anal 15:79–86MathSciNet CrossRef MATH
    47.Cao J (1999) Global stability analysis in delayed cellular neural networks. Phys Rev E 59:5940–5944MathSciNet CrossRef
    48.Yang X, Song Q, Liu Y, Zhao Z (2014) Finite-time stability analysis of fractional-order neural networks with delay. Neurocomputing. doi:10.​1016/​j.​neucom.​2014.​11.​023i
    49.Ke Y, Miao C (2014) Stability analysis of fractional-order CohenCGrossberg neural networks with time delay. Int J Comput Math. doi:10.​1080/​00207160.​2014.​935734
    50.Wu R, Lu Y, Chen L (2015) Finite-time stability of fractional delayed neural networks. Neurocomputing 149:700–707CrossRef
  • 作者单位:Liping Chen (1)
    Cong Liu (1)
    Ranchao Wu (2)
    Yigang He (1)
    Yi Chai (3)

    1. School of Electrical Engineering and Automation, Hefei University of Technology, Hefei, 230009, China
    2. School of Mathematics, Anhui University, Hefei, 230039, China
    3. School of Automation, Chongqing University, Chongqing, 400044, China
  • 刊物类别:Computer Science
  • 刊物主题:Simulation and Modeling
  • 出版者:Springer London
  • ISSN:1433-3058
文摘
Finite-time stabilities of a class of fractional-order neural networks delayed systems with order \(\alpha {:}\) \(0<\alpha \le 0.5\) and \(0.5<\alpha <1\) are addressed in this paper, respectively. By using inequality technique, two new delay-dependent sufficient conditions ensuring stability of such fractional-order neural networks over a finite-time interval are obtained. Obtained conditions are less conservative than that given in the earlier references. Two numerical examples are given to show the effectiveness of our proposed method.

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