Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability

Authors:
Yan Li;YangQuan Chen;Igor Podlubny
Affiliations:
Institute of Applied Math, School of Mathematics and System Sciences, Shandong University, Jinan 250100, PR China and Center for Self-Organizing and Intelligent Systems (CSOIS), Electrical and Com ...;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:
Computers & Mathematics with Applications
Year:
2010

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Abstract

Stability of fractional-order nonlinear dynamic systems is studied using Lyapunov direct method with the introductions of Mittag-Leffler stability and generalized Mittag-Leffler stability notions. With the definitions of Mittag-Leffler stability and generalized Mittag-Leffler stability proposed, the decaying speed of the Lyapunov function can be more generally characterized which include the exponential stability and power-law stability as special cases. Finally, four worked out examples are provided to illustrate the concepts.