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Technical Brief

# Stabilization Conditions for a Class of Fractional-Order Nonlinear Systems

[+] Author and Article Information
Sunhua Huang

Department of Electrical Engineering,
Northwest A&F University,
Yangling, Shaanxi 712100, China;
Key Laboratory of Agricultural Soil and
Water Engineering in Arid and Semiarid Areas,
Ministry of Education,
Northwest A&F University,
Yangling, Shaanxi 712100, China

Bin Wang

Department of Electrical Engineering,
Northwest A&F University,
Yangling, Shaanxi 712100, China;
Key Laboratory of Agricultural Soil and
Water Engineering in Arid and Semiarid Areas,
Ministry of Education,
Northwest A&F University,
Yangling, Shaanxi 712100, China
e-mail: binwang@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 August 18, 2018; final manuscript received February 26, 2019; published online March 14, 2019. Assoc. Editor: Bernard Brogliato.

J. Comput. Nonlinear Dynam 14(5), 054501 (Mar 14, 2019) (6 pages) Paper No: CND-18-1369; doi: 10.1115/1.4042999 History: Received August 18, 2018; Revised February 26, 2019

## Abstract

The stabilization problem of fractional-order nonlinear systems for $0<α<1$ is studied in this paper. Based on Mittag-Leffler function and the Lyapunov stability theorem, two practical stability conditions that ensure the stabilization of a class of fractional-order nonlinear systems are proposed. These stability conditions are given in terms of linear matrix inequalities and are easy to implement. Moreover, based on these conditions, the method for the design of state feedback controllers is given, and the conditions that enable the fractional-order nonlinear closed-loop systems to assure stability are provided. Finally, a representative case is employed to confirm the validity of the designed scheme.

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## Figures

Fig. 1

State trajectories of the fractional-order Chen system

Fig. 2

Stabilization of the nonlinear fractional-order Chen system with α = 0.5

Fig. 3

State trajectories of the controlled nonlinear fractional-order Chen system with α = 0.5

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