Stability results for fractional differential equations with applications to control processing

@inproceedings{Matignon1996StabilityRF,
  title={Stability results for fractional differential equations with applications to control processing},
  author={Denis Matignon},
  year={1996}
}
In this paper, stability results of main concern for control theory are given for finite-dimensional linear fractional differential systems. For fractional differential systems in state-space form, both internal and external stabilities are investigated. For fractional differential systems in polynomial representation, external stability is thoroughly examined. Our main qualitative result is that stabilities are guaranteed iff the roots of some polynomial lie outside the closed angular sector… CONTINUE READING

Citations

Publications citing this paper.
SHOWING 1-10 OF 621 CITATIONS

Boundedness and convergence on fractional order systems

  • J. Computational Applied Mathematics
  • 2016
VIEW 6 EXCERPTS
CITES METHODS & BACKGROUND
HIGHLY INFLUENCED

Recursive Set Membership Estimation for Output-Error Fractional Models with Unknown-But-Bounded Errors

  • Applied Mathematics and Computer Science
  • 2016
VIEW 4 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

FILTER CITATIONS BY YEAR

1996
2019

CITATION STATISTICS

  • 54 Highly Influenced Citations

  • Averaged 57 Citations per year from 2017 through 2019

References

Publications referenced by this paper.
SHOWING 1-10 OF 22 REFERENCES

ecomposi- tion modale fractionnaire de l' equation des on- des avec pertes viscothermiques. In Journ ees d' Etudes : les syst emes d'ordre non entier en automatique

  • GdR Auto cnrs,
  • 1995
VIEW 7 EXCERPTS
HIGHLY INFLUENTIAL

Fractional derivation operators: eigenfunctions and their asymptotic properties. Control, Optimisation and Calculus of Varia

D. Matignon
  • 1996
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

Sur la repr esentation ana- lytique d'une branche uniforme d'une fonction monog ene

G. Mittag-Le er
  • Acta Math.,
  • 1904
VIEW 2 EXCERPTS
HIGHLY INFLUENTIAL

Analysis of fractional di erential equations by algebraic means

D. Matignon
  • 1996
VIEW 3 EXCERPTS

D erivateur g en eralis e et repr esenta- tion g en eralis ee des syst emes lin eaires

F. Nanot
  • Th ese de Doctorat,
  • 1996
VIEW 1 EXCERPT

Fractional modal decomposition of a boundary-controlled-and-observed in nite- dimensional linear system

D. Matignon
  • 1996

Some results on controllability and observability of nite-dimensional fractional di erential systems

D. Matignon, B. d'Andr ea-Novel
  • 1996
VIEW 1 EXCERPT

La d erivation non enti ere : th eorie, synth ese, applications. s erie Automa- tique

A. Oustaloup
  • Editions Herm es,
  • 1995
VIEW 1 EXCERPT