On the structure at infinity of linear delay systems with application to the disturbance decoupling problem

Rabah Rabah; Michel Malabre

Kybernetika (1999)

  • Volume: 35, Issue: 6, page [668]-680
  • ISSN: 0023-5954

Abstract

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The disturbance decoupling problem is studied for linear delay systems. The structural approach is used to design a decoupling precompensator. The realization of the given precompensator by static state feedback is studied. Using various structural and geometric tools, a detailed description of the feedback is given, in particular, derivative of the delayed disturbance can be needed in the realization of the precompensator.

How to cite

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Rabah, Rabah, and Malabre, Michel. "On the structure at infinity of linear delay systems with application to the disturbance decoupling problem." Kybernetika 35.6 (1999): [668]-680. <http://eudml.org/doc/33454>.

@article{Rabah1999,
abstract = {The disturbance decoupling problem is studied for linear delay systems. The structural approach is used to design a decoupling precompensator. The realization of the given precompensator by static state feedback is studied. Using various structural and geometric tools, a detailed description of the feedback is given, in particular, derivative of the delayed disturbance can be needed in the realization of the precompensator.},
author = {Rabah, Rabah, Malabre, Michel},
journal = {Kybernetika},
keywords = {linear delay system; static state feedback; decoupling problem; disturbance; linear delay system; static state feedback; decoupling problem; disturbance},
language = {eng},
number = {6},
pages = {[668]-680},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On the structure at infinity of linear delay systems with application to the disturbance decoupling problem},
url = {http://eudml.org/doc/33454},
volume = {35},
year = {1999},
}

TY - JOUR
AU - Rabah, Rabah
AU - Malabre, Michel
TI - On the structure at infinity of linear delay systems with application to the disturbance decoupling problem
JO - Kybernetika
PY - 1999
PB - Institute of Information Theory and Automation AS CR
VL - 35
IS - 6
SP - [668]
EP - 680
AB - The disturbance decoupling problem is studied for linear delay systems. The structural approach is used to design a decoupling precompensator. The realization of the given precompensator by static state feedback is studied. Using various structural and geometric tools, a detailed description of the feedback is given, in particular, derivative of the delayed disturbance can be needed in the realization of the precompensator.
LA - eng
KW - linear delay system; static state feedback; decoupling problem; disturbance; linear delay system; static state feedback; decoupling problem; disturbance
UR - http://eudml.org/doc/33454
ER -

References

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  1. Hautus M. L. J., The formal Laplace transform for smooth linear systems, In: Proc. of Internat. Symposium on Mathematical Systems Theory, Udine 1975 (Lecture Notes in Economics and Mathematical Systems 131), Springer–Verlag, Berlin pp. 29–47 (1975) MR0682787
  2. Malabre M., Rabah R., On infinite zeros for infinite dimensional systems, In: Progress in Systems and Control Theory 3, Realiz. Model. in Systems Theory, Vol. 1, Birkhaüser, Boston 1990, pp. 19–206 (1990) MR1115331
  3. Malabre M., Rabah R., Structure at infinity, model matching and disturbance rejection for linear systems with delays, Kybernetika 29 (1993), 5, 485–498 (1993) Zbl0805.93008MR1264881
  4. Moog C., Inversion, découplage, poursuite de modèle des systèmes non linéaires, PhD Thesis, ENSM, Nantes 1987 
  5. Picard P., Lafay J.-F., Kučera V., Model matching for linear systems with delays, In: Proc. of 13th IFAC Congress, San Francisco 1996, Vol. D, pp. 183–188 (1996) 
  6. Pandolfi L., 10.1007/BF01442228, Appl. Math. Optim. 14 (1986), 55–72 (1986) Zbl0587.93039MR0826852DOI10.1007/BF01442228
  7. Rabah R., Structural properties and controllability for delay systems of neutral type, In: Proc. of the IFAC Conference on System Structure and Control, Nantes 1995, pp. 354–359 (1995) 
  8. Rabah R., Malabre M., Structure at infinity for delay systems revisited, In: Proc. of IMACS and IEEE–SMC Multiconference CESA’96, Symposium on Modelling, Analysis and Simulation, Lille 1996, pp. 87–90 (1996) 
  9. Rabah R., Malabre M., A note on decoupling for linear infinite dimensional systems, In: Proc. 4th IFAC Conf. on System Structure and Control, Bucharest 1997, pp. 78–83 (1997) 
  10. Rabah R., Malabre M., The structure at infinity of linear delay systems and the row–by–row decoupling problem, In: Proc. of 7th IEEE Mediterranean Conference on Control and Automation, Haifa 1999, pp. 1845–1854 (1999) 
  11. Sename O., Rabah R., Lafay J.-F., 10.1016/0167-6911(94)00086-B, Systems Control Lett. 25 (1995), 387–395 (1995) Zbl0877.93053MR1343224DOI10.1016/0167-6911(94)00086-B
  12. Silverman L. M., Kitapçi A., System structure at infinity, In: Colloque National CNRS, Développement et Utilisation d’Outils et Modèles Mathématiques en Automatique des Systèmes et Traitement du Signal, Belle–Ile 1983, Ed. CNRS, Vol. 3, pp. 413–424 (1983) Zbl0529.93018MR0733951
  13. Tsoi A. C., Recent advances in the algebraic system theory of delay differential equations, In: Recent Theoretical Developments in Control (M. J. Gregson, ed.), Academic Press, New York 1978, pp. 67–127 (1978) Zbl0417.93003MR0534622
  14. Wonham W. M., Linear Multivariable Control: A Geometric Approach, Third edition. Springer–Verlag, New York 1985 Zbl0609.93001MR0770574

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