Stabilization of fractional exponential systems including delays

Catherine Bonnet; Jonathan R. Partington

Kybernetika (2001)

  • Volume: 37, Issue: 3, page [345]-353
  • ISSN: 0023-5954

Abstract

top
This paper analyzes the BIBO stability of fractional exponential delay systems which are of retarded or neutral type. Conditions ensuring stability are given first. As is the case for the classical class of delay systems these conditions can be expressed in terms of the location of the poles of the system. Then, in view of constructing robust BIBO stabilizing controllers, explicit expressions of coprime and Bézout factors of these systems are determined. Moreover, nuclearity is analyzed in a particular case.

How to cite

top

Bonnet, Catherine, and Partington, Jonathan R.. "Stabilization of fractional exponential systems including delays." Kybernetika 37.3 (2001): [345]-353. <http://eudml.org/doc/33539>.

@article{Bonnet2001,
abstract = {This paper analyzes the BIBO stability of fractional exponential delay systems which are of retarded or neutral type. Conditions ensuring stability are given first. As is the case for the classical class of delay systems these conditions can be expressed in terms of the location of the poles of the system. Then, in view of constructing robust BIBO stabilizing controllers, explicit expressions of coprime and Bézout factors of these systems are determined. Moreover, nuclearity is analyzed in a particular case.},
author = {Bonnet, Catherine, Partington, Jonathan R.},
journal = {Kybernetika},
keywords = {delay system; BIBO stability; delay system; BIBO stability},
language = {eng},
number = {3},
pages = {[345]-353},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Stabilization of fractional exponential systems including delays},
url = {http://eudml.org/doc/33539},
volume = {37},
year = {2001},
}

TY - JOUR
AU - Bonnet, Catherine
AU - Partington, Jonathan R.
TI - Stabilization of fractional exponential systems including delays
JO - Kybernetika
PY - 2001
PB - Institute of Information Theory and Automation AS CR
VL - 37
IS - 3
SP - [345]
EP - 353
AB - This paper analyzes the BIBO stability of fractional exponential delay systems which are of retarded or neutral type. Conditions ensuring stability are given first. As is the case for the classical class of delay systems these conditions can be expressed in terms of the location of the poles of the system. Then, in view of constructing robust BIBO stabilizing controllers, explicit expressions of coprime and Bézout factors of these systems are determined. Moreover, nuclearity is analyzed in a particular case.
LA - eng
KW - delay system; BIBO stability; delay system; BIBO stability
UR - http://eudml.org/doc/33539
ER -

References

top
  1. Bonnet C., Partington J. R., 10.1109/9.780415, IEEE Trans. Automat. Control 44 (1999), 1512–1521 (1999) MR1707048DOI10.1109/9.780415
  2. Bonnet C., Partington J. R., Analysis of fractional delay systems of retarded and neutral type, Preprint 2000 Zbl1007.93065MR2133473
  3. Bonnet C., Partington J. R., 10.1016/S0167-6911(00)00050-5, Systems Control Lett. 41 (2000), 167–174 Zbl0985.93048MR1831424DOI10.1016/S0167-6911(00)00050-5
  4. Curtain R. F., Zwart H. J., An Introduction to Infinite Dimensional Linear Systems Theory, Springer–Verlag, Berlin 1995 Zbl0839.93001MR1351248
  5. Glover K., Curtain R. F., Partington J. R., 10.1137/0326049, SIAM J. Control Optim. 26 (1988), 863–898 (1988) MR0948650DOI10.1137/0326049
  6. Gripenberg G., Londen S. O., Staffans O., Volterra Integral and Functional Equations, Cambridge University Press, Cambridge, U.K. 1990 Zbl1159.45001MR1050319
  7. Hille E., Phillips R. S., Functional analysis and semi-groups, American Mathematical Society, Providence, R. I., 1957 Zbl0392.46001MR0089373
  8. Hotzel R., Some stability conditions for fractional delay systems, J. Math. Systems, Estimation, and Control 8 (1998), 1–19 (1998) Zbl0913.93068MR1651287
  9. Loiseau J.-J., Mounier H., Stabilisation de l’équation de la chaleur commandée en flux, Systèmes Différentiels Fractionnaires, Modèles, Méthodes et Applications. ESAIM Proceedings 5 (1998), 131–144 (1998) Zbl0913.73052MR1665567
  10. Matignon D., Représentations en variables d’état de modèles de guides d’ondes avec dérivation fractionnaire, Thèse de doctorat, Univ. Paris XI, 1994 
  11. Partington J. R., An Introduction to Hankel Operators, Cambridge University Press, Cambridge, U.K. 1988 Zbl0668.47022MR0985586
  12. Weber E., Linear Transient Analysis, Volume II. Wiley, New York 1956 Zbl0073.21801MR0080524

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.