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Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. (English) Zbl 1189.34015
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:
 34A08 Fractional differential equations 26A33 Fractional derivatives and integrals (real functions) 34D20 Stability of ODE 37C75 Stability theory
Full Text:
##### References:
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