Mittag–Leffler stability of fractional order nonlinear dynamic systems

• Published in: Automatica (Oxford) Vol. 45; no. 8; pp. 1965 - 1969
• Main Authors: Li, Yan, Chen, YangQuan, Podlubny, Igor
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.08.2009; Elsevier
• Subjects: Applied sciences; Automation; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Dynamical systems; Exact sciences and technology; Fractional comparison principle; Fractional Lyapunov direct method; Fractional order dynamic system; Mittag–Leffler stability; Nonautonomous system; Nonlinear dynamics; Stability; Nonautonomous system; Fractional Lyapunov direct method; Fractional comparison principle; Fractional order dynamic system; Mittag–Leffler stability; Stability; Mittag-Leffler stability; Non linear control; Non autonomous system; Dynamical system; Fractional derivative; Lyapunov function
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2009.04.003

In this paper, 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.