This paper is mainly concerned with asymptotic stability for a class of fractional-order (FO) nonlinear system with application to stabilization of a fractional permanent magnet synchronous motor (PMSM). First of all, we discuss the stability problem of a class of fractional time-varying systems with nonlinear dynamics. By employing Gronwall–Bellman's inequality, Laplace transform and its inverse transform, and estimate forms of Mittag–Leffler (ML) functions, when the FO belongs to the interval (0, 2), several stability criterions for fractional time-varying system described by Riemann–Liouville's definition is presented. Then, it is generalized to stabilize a FO nonlinear PMSM system. Furthermore, it should be emphasized here that the asymptotic stability and stabilization of Riemann–Liouville type FO linear time invariant system with nonlinear dynamics is proposed for the first time. Besides, some problems about the stability of fractional time-varying systems in existing literatures are pointed out. Finally, numerical simulations are given to show the validness and feasibleness of our obtained stability criterions.
Asymptotic Stabilization of Fractional Permanent Magnet Synchronous Motor
Beijing University of Aeronautics
Beijing 100191, China
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received April 14, 2017; final manuscript received August 25, 2017; published online November 1, 2017. Assoc. Editor: Dumitru Baleanu.
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Guo, Y., and Ma, B. (November 1, 2017). "Asymptotic Stabilization of Fractional Permanent Magnet Synchronous Motor." ASME. J. Comput. Nonlinear Dynam. February 2018; 13(2): 021003. https://doi.org/10.1115/1.4037929
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