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Zbl 1189.34015
Li, Yan; Chen, Yangquan; Podlubny, Igor
Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. (English)
[J] Comput. Math. Appl. 59, No. 5, 1810-1821 (2010). ISSN 0898-1221

Summary: Stability of fractional-order nonlinear dynamic systems is studied using Lyapunov direct method with the introductions of Mittag-Leffler stability and generalized Mittag-Leffler stability notions. With the definitions of Mittag-Leffler stability and generalized Mittag-Leffler stability proposed, the decaying speed of the Lyapunov function can be more generally characterized which include the exponential stability and power-law stability as special cases. Finally, four worked out examples are provided to illustrate the concepts.

MSC 2000:: *34A08
26A33 Fractional derivatives and integrals (real functions)
34D20 Lyapunov stability of ODE
37C75 Stability theory

Keywords: fractional-order dynamic system; nonautonomous system; fractional Lyapunov direct method; generalized Mittag-Leffler stability; fractional comparison principle

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Zentralblatt MATH Berlin [Germany]