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A linearized stability theorem for nonlinear delay fractional differential equations

journal contribution
posted on 2018-09-01, 00:00 authored by H T Tuan, Hieu TrinhHieu Trinh
IEEE In this paper, we prove a theorem of linearized asymptotic stability for nonlinear fractional differential equations with a time delay. By using the method of linearization of a nonlinear equation along an orbit (Lyapunov's first method), we show that an equilibrium of a nonlinear Caputo fractional delay differential equation is asymptotically stable if its linearization at the equilibrium is asymptotically stable. Our approach is based on a technique which converts the linear part of the equation into a diagonal one. Then by using the properties of generalized Mittag-Leffler functions, the construction of an associated Lyapunov-Perron operator and the Banach contraction mapping theorem, we obtain the desired result.

History

Journal

IEEE transactions on automatic control

Volume

63

Issue

9

Pagination

3180 - 3186

Publisher

IEEE

Location

Piscataway, N.J.

ISSN

0018-9286

Language

eng

Publication classification

C1 Refereed article in a scholarly journal; C Journal article

Copyright notice

2017, IEEE