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Mittag-Leffler stability of fractional order nonlinear dynamic systems. (English) Zbl 1185.93062
Summary: 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
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