Technical communique: Mittag-Leffler stability of fractional order nonlinear dynamic systems

Authors:
Yan Li;YangQuan Chen;Igor Podlubny
Affiliations:
Institute of Applied Math, School of Mathematics and System Sciences, Shandong University, Jinan 250100, PR China;Center for Self-Organizing and Intelligent Systems (CSOIS), Electrical and Computer Engineering Department, Utah State University, Logan, UT 84322-4160, USA;Department of Applied Informatics and Process Control, Faculty BERG, Technical University of Kosice, B. Nemcovej 3, 04200 Kosice, Slovak Republic
Venue:
Automatica (Journal of IFAC)
Year:
2009

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Abstract

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.