This paper, composed of two parts, addresses the stability of linear commensurate order fractional systems, Dn (X) = A X 0 < n < 1, using the infinite state approach. Whereas Part 1 has been dedicated to the definition of fractional systems energy, Part 2 deals with the derivation of a stability condition. When the eigenvalues of A are real, the modal representation shows that system energy is the sum of independent modal energies, so the derivation of a stability condition is straightforward in this case. On the contrary, when the eigenvalues are complex with positive real parts, unusual energy dynamics depending on initial conditions prevent direct derivation of a stability condition. Thus, an indirect method is proposed to formulate a stability condition in the complex eigenvalues case.
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ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 4–7, 2013
Portland, Oregon, USA
Conference Sponsors:
- Design Engineering Division
- Computers and Information in Engineering Division
ISBN:
978-0-7918-5591-1
PROCEEDINGS PAPER
Lyapunov Stability of Linear Fractional Systems: Part 2 — Derivation of a Stability Condition
Jean-Claude Trigeassou,
Jean-Claude Trigeassou
University of Bordeaux, Bordeaux, France
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Nezha Maamri,
Nezha Maamri
University of Poitiers, Poitiers, France
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Alain Oustaloup
Alain Oustaloup
University of Bordeaux, Bordeaux, France
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Jean-Claude Trigeassou
University of Bordeaux, Bordeaux, France
Nezha Maamri
University of Poitiers, Poitiers, France
Alain Oustaloup
University of Bordeaux, Bordeaux, France
Paper No:
DETC2013-12830, V004T08A026; 10 pages
Published Online:
February 12, 2014
Citation
Trigeassou, J, Maamri, N, & Oustaloup, A. "Lyapunov Stability of Linear Fractional Systems: Part 2 — Derivation of a Stability Condition." Proceedings of the ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 4: 18th Design for Manufacturing and the Life Cycle Conference; 2013 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications. Portland, Oregon, USA. August 4–7, 2013. V004T08A026. ASME. https://doi.org/10.1115/DETC2013-12830
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