Studying on the stability of fractional-order nonlinear system

In this paper, we study the properties of the Mittag–Leffler function and propose an approach for calculating the maximum norm of eigenvalue of Jacobian matrix of nonlinear system. Then a simple approach is proposed for judging the stability of fractional nonlinear system. Based on the approach, the...

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Bibliographic Details
Published in:Nonlinear dynamics 2012-10, Vol.70 (1), p.475-479
Main Authors: Zhao, Ling-Dong, Hu, Jian-Bing, Fang, Jian-An, Zhang, Wen-Bing
Format: Article
Language:English
Subjects:
Automotive Engineering
Classical Mechanics
Control
Decay rate
Dynamical Systems
Eigenvalues
Engineering
Jacobi matrix method
Jacobian matrix
Mathematical analysis
Mechanical Engineering
Nonlinear systems
Original Paper
Stability
Vibration
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Summary:In this paper, we study the properties of the Mittag–Leffler function and propose an approach for calculating the maximum norm of eigenvalue of Jacobian matrix of nonlinear system. Then a simple approach is proposed for judging the stability of fractional nonlinear system. Based on the approach, the maximum decay rate of fractional nonlinear system can be calculated. Finally, some examples are provided to illustrate the approach.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-012-0469-0