Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability.

*(English)*Zbl 1189.34015Summary: 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:

34A08 | Fractional ordinary differential equations |

26A33 | Fractional derivatives and integrals |

34D20 | Stability of solutions to ordinary differential equations |

37C75 | Stability theory for smooth dynamical systems |

##### Keywords:

fractional-order dynamic system; nonautonomous system; fractional Lyapunov direct method; generalized Mittag-Leffler stability; fractional comparison principle
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\textit{Y. Li} et al., Comput. Math. Appl. 59, No. 5, 1810--1821 (2010; Zbl 1189.34015)

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##### References:

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