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

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Abstract

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.

Keywords

Fractional-order dynamic system
Nonautonomous system
Fractional Lyapunov direct method
Generalized Mittag–Leffler stability
Fractional comparison principle

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