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Zbl 1185.93062
Li, Yan; Chen, Yangquan; Podlubny, Igor
Mittag-Leffler stability of fractional order nonlinear dynamic systems. (English)
[J] Automatica 45, No. 8, 1965-1969 (2009). ISSN 0005-1098

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 2000:: *93C30 Control systems governed by other functional relations
34A08
93C10 Nonlinear control systems
93C30 Control systems governed by other functional relations
93D05 Lyapunov and other classical stabilities of control systems

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

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Zentralblatt MATH Berlin [Germany]