Stability Analysis of Fractional-Order Nonlinear Systems with Delay | Zendy

Yu Wang | Zendy; Tianzeng Li | Zendy

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Stability Analysis of Fractional-Order Nonlinear Systems with Delay

Author(s) -

Yu Wang,

Tianzeng Li

Publication year - 2014

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2014/301235

Subject(s) - laplace transform , nonlinear system , mathematics , stability (learning theory) , fractional order system , fractional calculus , order (exchange) , control theory (sociology) , universality (dynamical systems) , lyapunov function , mathematical analysis , computer science , physics , control (management) , finance , quantum mechanics , machine learning , artificial intelligence , economics

Stability analysis of fractional-order nonlinear systems with delay is studied. We propose the definition of Mittag-Leffler stability of time-delay system and introduce the fractional Lyapunov direct method by using properties of Mittag-Leffler function and Laplace transform. Then some new sufficient conditions ensuring asymptotical stability of fractional-order nonlinear system with delay are proposed firstly. And the application of Riemann-Liouville fractional-order systems is extended by the fractional comparison principle and the Caputo fractional-order systems. Numerical simulations of an example demonstrate the universality and the effectiveness of the proposed method

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