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Research Papers

# Stability of Nonlinear Fractional-Order Time Varying Systems

[+] Author and Article Information
Sunhua Huang, Runfan Zhang

Institute of Water Resources and
Hydropower Research,
Northwest A&F University,
Yangling 712100, Shaanxi, China

Diyi Chen

Institute of Water Resources and
Hydropower Research,
Northwest A&F University,
Yangling 712100, Shaanxi, China
e-mail: diyichen@nwsuaf.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 8, 2015; final manuscript received September 12, 2015; published online October 23, 2015. Assoc. Editor: Hiroshi Yabuno.

J. Comput. Nonlinear Dynam 11(3), 031007 (Oct 23, 2015) (9 pages) Paper No: CND-15-1040; doi: 10.1115/1.4031587 History: Received February 08, 2015; Revised September 12, 2015

## Abstract

This paper is concerned with the stability of nonlinear fractional-order time varying systems with Caputo derivative. By using Laplace transform, Mittag-Leffler function, and the Gronwall inequality, the sufficient condition that ensures local stability of fractional-order systems with fractional order $α$ : $0<α≤1$ and $1<α<2$ is proposed, respectively. Moreover, the condition of the stability of fractional-order systems with a state-feedback controller is been put forward. Finally, a numerical example is presented to show the validity and feasibility of the proposed method.

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## Figures

Fig. 1

Stability domain of fractional-order system with fractional order 0 < α ≤ 1

Fig. 2

Stability domain of fractional-order time varying system with fractional order 1 < α < 2

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