This study is interested in the stability and stabilization of a class of fractional-order nonlinear systems with Caputo derivatives. Based on the properties of the Laplace transform, Mittag-Leffler function, Jordan decomposition, and Grönwall's inequality, some sufficient conditions that ensure local stability and stabilization of a class of fractional-order nonlinear systems under the Caputo derivative with are presented. Finally, typical instances, including the fractional-order three-dimensional (3D) nonlinear system and the fractional-order four-dimensional (4D) nonlinear hyperchaos, are implemented to demonstrate the feasibility and validity of the proposed method.
Stability and Stabilization of a Class of Fractional-Order Nonlinear Systems for 1 < α < 2
Northwest A&F University,
Yangling 712100, Shaanxi, China
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 19, 2016; final manuscript received November 6, 2017; published online January 10, 2018. Editor: Bala Balachandran.
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Huang, S., and Wang, B. (January 10, 2018). "Stability and Stabilization of a Class of Fractional-Order Nonlinear Systems for 1 < α < 2." ASME. J. Comput. Nonlinear Dynam. March 2018; 13(3): 031003. https://doi.org/10.1115/1.4038443
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