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Lyapunov Stability of Linear Fractional Systems: Part 2 — Derivation of a Stability Condition

[+] Author Affiliations
Jean-Claude Trigeassou, Alain Oustaloup

University of Bordeaux, Bordeaux, France

Nezha Maamri

University of Poitiers, Poitiers, France

Paper No. DETC2013-12830, pp. V004T08A026; 10 pages
doi:10.1115/DETC2013-12830
From:
  • 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
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5591-1
  • Copyright © 2013 by ASME

abstract

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.

Copyright © 2013 by ASME
Topics: Stability

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