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Discontinuity, Nonlinearity, and Complexity 5(4) (2016) 415--425 | DOI:10.5890/DNC.2016.12.007

Tianzeng Li$^{1}$,$^{2}$, Yu Wang$^{1}$,$^{3}$, Yong Yang

1School of Science, Sichuan University of Science and Engineering, Zigong 643000, China

2Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing, Zigong 643000, China

3Artificial Intelligence Key Laboratory of Sichuan Province, Zigong, 643000, China

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Abstract

In this letter stability analysis of fractional order nonlinear systems is studied. An extension of Lyapunov direct method for fractional order systems is proposed by using the properties of Mittag-Leffler function and Laplace transform. Some new sufficient conditions which ensure local exponential stability of fractional order nonlinear systems are proposed firstly. And we apply these conditions to the Riemann-Liouville fractional order systems by using fractional comparison principle. Finally, three examples are provided to illustrate the validity of the proposed approach.

Acknowledgments

The work is supported by Found of Science &Technology Department of Sichuan Province (Grant No.2016JQ0046), Artificial Intelligence Key Laboratory of Sichuan Province (Grant No.2016RYJ06), Found of Sichuan University of Science and Engineering (Grant 2014PY06, 2015RC10), the Opening Project of Sichuan Province University Key Laborstory of Bridge Non-destruction Detecting and Engineering Computing (Grant No.2015QYJ02, 2014QZJ03), Opening Project of Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things (Grant No.2016WYJ04).

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