Mittag-Leffler stability of fractional order nonlinear dynamic systems.

*(English)*Zbl 1185.93062Summary: We propose the definition of Mittag-Leffler stability and introduce the fractional Lyapunov direct method. Fractional comparison principle is introduced and the application of Riemann-Liouville fractional order systems is extended by using Caputo fractional order systems. Two illustrative examples are provided to illustrate the proposed stability notion.

##### MSC:

93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |

34A08 | Fractional ordinary differential equations and fractional differential inclusions |

93C10 | Nonlinear systems in control theory |

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

##### Keywords:

fractional order dynamic system; nonautonomous system; fractional Lyapunov direct method; Mittag-Leffler stability; fractional comparison principle
Full Text:
DOI

##### References:

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