Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag–Leffler stability
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Momani, 2004, Lyapunov stability solutions of fractional integrodifferential equations, International Journal of Mathematics and Mathematical Sciences, 47, 2503, 10.1155/S0161171204312366
Zhang, 2005, Extension of Lyapunov second method by fractional calculus, Pure and Applied Mathematics, 3, 1008
Vasily E. Tarasov, Fractional stability, 2007. Available online: http://arxiv.org/abs/0711.2117v1
YangQuan Chen, Ubiquitous fractional order controls? in: Proceedings of the Second IFAC Workshop on Fractional Differentiation and Its Applications, Porto, Portugal, 2006
Jocelyn Sabatier, On stability of fractional order systems, in: Plenary Lecture VIII on 3rd IFAC Workshop on Fractional Differentiation and its Applications, Ankara, Turkey, 05–07 November, 2008
Jocelyn Sabatier, Mathieu Merveillaut, Rachid Malti, Alain Oustaloup, On a representation of fractional order systems: Interests for the initial condition problem, Paper accepted to the next IFAC Fractional Derivative and its Applications Workshop, FDA 08, 5–7 November, Ankara, Turkey
Manuel D. Ortigueira, Fernando J. Coito, Initial conditions: What are we talking about? Paper accepted to the next IFAC Fractional Derivative and its Applications Workshop, FDA 08, 5–7 November, Ankara, Turkey
Yan Li, YangQuan Chen, Igor Podlubny, Yongcan Cao, Mittag-leffler stability of fractional order nonlinear dynamic systems, Paper accepted to the next IFAC Fractional Derivative and its Applications Workshop, FDA 08, 5–7 November, Ankara, Turkey
Chen, 2002, Analytical stability bound for a class of delayed fractional order dynamic systems, Nonlinear Dynamics, 29, 191, 10.1023/A:1016591006562
Podlubny, 1999, Fractional-order systems and PIλDμ-Controllers, IEEE Transactions on Automatic Control, 44, 208, 10.1109/9.739144
Podlubny, 1999
Sabatier, 2007
Xu, 2006, Intermediate processes and critical phenomena: Theory, method and progress of fractional operators and their applications to modern mechanics, Science in China: Series G Physics, Mechanics and Astronomy, 49, 257
Sastry, 1989
Appleby, 2002, On the non-exponential convergence of asymptotically stable solutions of linear scalar volterra integro-differential equations, Journal of Integral Equations and Applications, 14, 109, 10.1216/jiea/1031328362
Miller, 2001, Completely monotonic functions, Integral Transforms and Special Functions, 12, 389, 10.1080/10652460108819360
Khalil, 2002