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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 ordinary differential equations
26A33 Fractional derivatives and integrals
34D20 Stability of solutions to ordinary differential equations
37C75 Stability theory for smooth dynamical systems
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