Mittag–Leffler stability of fractional order nonlinear dynamic systems

Yan Li; YangQuan Chen; Igor Podlubny

doi:10.1016/j.automatica.2009.04.003

Mittag–Leffler stability of fractional order nonlinear dynamic systems

Automatica ◽

10.1016/j.automatica.2009.04.003 ◽

2009 ◽

Vol 45 (8) ◽

pp. 1965-1969 ◽

Cited By ~ 790

Author(s):

Yan Li ◽

YangQuan Chen ◽

Igor Podlubny

Keyword(s):

Fractional Order ◽

Dynamic Systems ◽

Nonlinear Dynamic ◽

Nonlinear Dynamic Systems

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Application of an operational method of non-classical type for the analysis of transient processes in nonlinear dynamic systems of whole and fractional order

Electronics and Control Systems ◽

10.18372/1990-5548.28.872 ◽

2011 ◽

Vol 2 (28) ◽

Author(s):

Е.В. Киркач

Keyword(s):

Fractional Order ◽

Dynamic Systems ◽

Nonlinear Dynamic ◽

Transient Processes ◽

Nonlinear Dynamic Systems ◽

Classical Type ◽

Operational Method

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New Results on Exponential Stability of Fractional Order Nonlinear Dynamic Systems

The interdisciplinary journal of Discontinuity Nonlinearity and Complexity ◽

10.5890/dnc.2016.12.007 ◽

2016 ◽

Vol 5 (4) ◽

pp. 415-425 ◽

Cited By ~ 1

Author(s):

Tianzeng Li ◽

Yu Wang ◽

Yong Yang

Keyword(s):

Exponential Stability ◽

Fractional Order ◽

Dynamic Systems ◽

Nonlinear Dynamic ◽

Nonlinear Dynamic Systems

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Fractional-order Hammerstein state-space modeling of nonlinear dynamic systems from input–output measurements

ISA Transactions ◽

10.1016/j.isatra.2019.06.015 ◽

2020 ◽

Vol 96 ◽

pp. 177-184

Author(s):

Mohammad-Reza Rahmani ◽

Mohammad Farrokhi

Keyword(s):

State Space ◽

Fractional Order ◽

Dynamic Systems ◽

Nonlinear Dynamic ◽

Nonlinear Dynamic Systems ◽

Input Output ◽

Space Modeling ◽

State Space Modeling

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Integer-fractional decomposition and stability analysis of fractional-order nonlinear dynamic systems using homotopy singular perturbation method

Mathematics of Control Signals and Systems ◽

10.1007/s00498-020-00268-6 ◽

2020 ◽

Vol 32 (4) ◽

pp. 517-542

Author(s):

Mahnaz Abolvafaei ◽

Soheil Ganjefar

Keyword(s):

Stability Analysis ◽

Singular Perturbation ◽

Perturbation Method ◽

Fractional Order ◽

Dynamic Systems ◽

Nonlinear Dynamic ◽

Nonlinear Dynamic Systems ◽

Singular Perturbation Method

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Comments on “Mittag-Leffler stability of fractional order nonlinear dynamic systems [Automatica 45(8) (2009) 1965–1969]”

Automatica ◽

10.1016/j.automatica.2016.09.023 ◽

2017 ◽

Vol 75 ◽

pp. 329 ◽

Cited By ~ 12

Author(s):

Omar Naifar ◽

Abdellatif Ben Makhlouf ◽

Mohamed Ali Hammami

Keyword(s):

Fractional Order ◽

Dynamic Systems ◽

Nonlinear Dynamic ◽

Nonlinear Dynamic Systems

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T-S fuzzy models based approximation for general fractional order nonlinear dynamic systems

2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) ◽

10.1109/fuzz-ieee.2014.6891524 ◽

2014 ◽

Author(s):

Yong Wang ◽

Yiheng Wei ◽

Min Zhu ◽

Mengmeng Liu ◽

Cheng Peng ◽

...

Keyword(s):

Fractional Order ◽

Dynamic Systems ◽

Nonlinear Dynamic ◽

Nonlinear Dynamic Systems ◽

Fuzzy Models

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Reply to “Comments on ‘Mittag-Leffler stability of fractional order nonlinear dynamic systems’ [Automatica 45(8) (2009) 1965–1969]”

Automatica ◽

10.1016/j.automatica.2016.09.026 ◽

2017 ◽

Vol 75 ◽

pp. 330 ◽

Cited By ~ 1

Author(s):

Yan Li ◽

YangQuan Chen ◽

Igor Podlubny

Keyword(s):

Fractional Order ◽

Dynamic Systems ◽

Nonlinear Dynamic ◽

Nonlinear Dynamic Systems

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Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag–Leffler stability

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2009.08.019 ◽

2010 ◽

Vol 59 (5) ◽

pp. 1810-1821 ◽

Cited By ~ 728

Author(s):

Yan Li ◽

YangQuan Chen ◽

Igor Podlubny

Keyword(s):

Fractional Order ◽

Dynamic Systems ◽

Nonlinear Dynamic ◽

Direct Method ◽

Nonlinear Dynamic Systems ◽

Lyapunov Direct Method

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Analysis of fractional‐order nonlinear dynamic systems under Caputo differential operator

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.7454 ◽

2021 ◽

Author(s):

Abdullahi Yusuf ◽

Bahar Acay ◽

Mustafa Inc

Keyword(s):

Differential Operator ◽

Fractional Order ◽

Dynamic Systems ◽

Nonlinear Dynamic ◽

Nonlinear Dynamic Systems ◽

Caputo Differential Operator

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Recovery of State Vector of Nonlinear Dynamic Systems

Journal of Automation and Information Sciences ◽

10.1615/jautomatinfscien.v39.i9.10 ◽

2007 ◽

Vol 39 (9) ◽

pp. 1-15

Author(s):

Vsevold M. Kuntsevich

Keyword(s):

Dynamic Systems ◽

Nonlinear Dynamic ◽

State Vector ◽

Nonlinear Dynamic Systems

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