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Stability and stabilization of a class of fractional-order nonlinear systems for 1<?<2

[+] Author and Article Information
Sunhua Huang

Department of Electrical Engineering, Northwest A&F University, Shaanxi Yangling 712100, P. R. China
976961548@qq.com

Bin Wang

Department of Electrical Engineering, Northwest A&F University, Shaanxi Yangling 712100, P. R. China
binwang@nwsuaf.edu.cn

1Corresponding author.

ASME doi:10.1115/1.4038443 History: Received September 19, 2016; Revised November 06, 2017

Abstract

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, sufficient conditions that ensure local stability and stabilization of a class of fractional-order nonlinear systems under the Caputo derivative with 1<a<2 are presented. Finally, typical instances, including the fractional-order three-dimensional (3D) nonlinear system and the fractional-order 4D nonlinear hyperchaos, are implemented to demonstrate the feasibility and validity of the proposed method.

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