Control of distributed delay systems with uncertainties: a generalized Popov theory approach

Dan Ivanescu; Silviu-Iulian Niculescu; Jean-Michel Dion; Luc Dugard

Kybernetika (2001)

  • Volume: 37, Issue: 3, page 325-343
  • ISSN: 0023-5954

Abstract

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The paper deals with the generalized Popov theory applied to uncertain systems with distributed time delay. Sufficient conditions for stabilizing this class of delayed systems as well as for γ -attenuation achievement are given in terms of algebraic properties of a Popov system via a Liapunov–Krasovskii functional. The considered approach is new in the context of distributed linear time-delay systems and gives some interesting interpretations of H ∞ memoryless control problems in terms of Popov triplets and associated objects. The approach is illustrated via numerical examples. Dedicated to Acad. Vlad Ionescu, in memoriam.

How to cite

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Ivanescu, Dan, et al. "Control of distributed delay systems with uncertainties: a generalized Popov theory approach." Kybernetika 37.3 (2001): 325-343. <http://eudml.org/doc/33538>.

@article{Ivanescu2001,
abstract = {The paper deals with the generalized Popov theory applied to uncertain systems with distributed time delay. Sufficient conditions for stabilizing this class of delayed systems as well as for $\gamma $-attenuation achievement are given in terms of algebraic properties of a Popov system via a Liapunov–Krasovskii functional. The considered approach is new in the context of distributed linear time-delay systems and gives some interesting interpretations of $H^\infty $ memoryless control problems in terms of Popov triplets and associated objects. The approach is illustrated via numerical examples. Dedicated to Acad. Vlad Ionescu, in memoriam.},
author = {Ivanescu, Dan, Niculescu, Silviu-Iulian, Dion, Jean-Michel, Dugard, Luc},
journal = {Kybernetika},
keywords = {Popov theory; time-delay system; uncertainty; Popov theory; time-delay system; uncertainty},
language = {eng},
number = {3},
pages = {325-343},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Control of distributed delay systems with uncertainties: a generalized Popov theory approach},
url = {http://eudml.org/doc/33538},
volume = {37},
year = {2001},
}

TY - JOUR
AU - Ivanescu, Dan
AU - Niculescu, Silviu-Iulian
AU - Dion, Jean-Michel
AU - Dugard, Luc
TI - Control of distributed delay systems with uncertainties: a generalized Popov theory approach
JO - Kybernetika
PY - 2001
PB - Institute of Information Theory and Automation AS CR
VL - 37
IS - 3
SP - 325
EP - 343
AB - The paper deals with the generalized Popov theory applied to uncertain systems with distributed time delay. Sufficient conditions for stabilizing this class of delayed systems as well as for $\gamma $-attenuation achievement are given in terms of algebraic properties of a Popov system via a Liapunov–Krasovskii functional. The considered approach is new in the context of distributed linear time-delay systems and gives some interesting interpretations of $H^\infty $ memoryless control problems in terms of Popov triplets and associated objects. The approach is illustrated via numerical examples. Dedicated to Acad. Vlad Ionescu, in memoriam.
LA - eng
KW - Popov theory; time-delay system; uncertainty; Popov theory; time-delay system; uncertainty
UR - http://eudml.org/doc/33538
ER -

References

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  1. Cheres E., Gutman, S., Palmor Z. J., 10.1109/9.40753, IEEE Trans. Automat. Control 34 (1989), 1199–1203 (1989) MR1020938DOI10.1109/9.40753
  2. Dion J.-M., Dugard L., Ivanescu D., Niculescu S.-I., Ionescu V., Robust H ∞ control of time-delay systems: A generalized Popov theory approach, In: Perspectives in Control Theory and applications, Springer–Verlag, Berlin 1998, pp. 61–82 (1998) Zbl0976.93066
  3. Dugard L., (eds.) E. I. Verriest, Stability and Control of Time–Delay Systems, (Lecture Notes in Computer Science 228.) Springer–Verlag, London 1997 Zbl0901.00019MR1482570
  4. Hale J. K., Lunel S. M. Verduyn, Introduction to Functional Differential Equations, (Applied Mathematical Sciences 99.) Springer–Verlag, Berlin 1991 MR1243878
  5. Ionescu V., Niculescu S.-I., Dion J.-M., Dugard, L., Li H., Generalized Popov theory applied to state-delayed systems, In: Proc. IFAC Conference on System Structure and Control, Nantes 1998, pp. 645–650 (1998) 
  6. Ionescu V., Niculescu S.-I., Woerdeman H., On ℒ 2 memoryless control of time-delay systems, In: Proc. 36th IEEE Conference on Decision and Control, San Diego 1997, pp. 1344–1349 (1997) 
  7. Ionescu V., Oară, C., Weiss M., Generalized Riccati Theory, Wiley, New York 1998 Zbl0915.34024
  8. Ionescu V., Weiss M., Continuous and discrete-time Riccati theory: a Popov function approach, Linear Algebra Appl. 193 (1993), 173–209 (193) MR1240278
  9. Ivanescu D., Niculescu S.-I., Dion J.-M., Dugard L., Control of Distributed Varying Delay Systems Using Generalized Popov Theory, Internal Note, LAG–98 
  10. Kojima A., Uchida, K., Shimemura E., 10.1109/9.250497, IEEE Trans. Automat. Control 38 (1993), 373–378 (1993) Zbl0773.93066MR1206835DOI10.1109/9.250497
  11. Kolmanovskii V. B., Nosov V. R., Stability of Functional Differential Equations, (Mathematics in Science and Engineering 180.) Academic Press, New York 1986 Zbl0593.34070MR0860947
  12. Lee J. H., Kim S. W., Kwon W. H., 10.1109/9.273356, IEEE Trans. Automat. Control 39 (1994), 159–162 (1994) MR1258692DOI10.1109/9.273356
  13. Niculescu S.-I., Souza C. E. de, Dion J.-M., Dugard L., Robust ℋ ∞ memoryless control for uncertain linear systems with time-varying delay, In: 3rd European Control Conference, Rome 1995, pp. 1814–1818 (1995) 
  14. Niculescu S.-I., Ionescu V., 10.1093/imamci/14.3.299, IMA J. Math. Control Inform. 14 (1997), 299–306 (1997) Zbl0886.93056MR1467584DOI10.1093/imamci/14.3.299
  15. Niculescu S.-I., Ionescu V., Ivănescu D., Dion J.-M., Dugard L., On generalized Popov theory for delay systems, In: 6th IEEE Mediteranean Conference, Sardaigne 1998 and Kybernetika 36 (2000), 2–20 (1998) MR1760884
  16. Niculescu S.-I., Ionescu, V., Woerdeman H., On the Popov theory for some classes of time-delay systems: A matrix pencil approach, In: MTNS’98, Padova 1998 
  17. Oară C., 10.1007/BF02140690, Numer. Algorithms 7 (1994), 355–377 (1994) MR1283105DOI10.1007/BF02140690
  18. Xie L., Souza C. E. de, Robust stabilization and disturbance attenuation for uncertain delay system, In: Proc. 2nd European Control Conference, Groningen 1993, pp. 667–672 (1993) 

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