Stability and stabilizability of a class of uncertain dynamical systems with delays

Mohammed Saadni; Driss Mehdi

International Journal of Applied Mathematics and Computer Science (2005)

  • Volume: 15, Issue: 3, page 321-329
  • ISSN: 1641-876X

Abstract

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This paper deals with a class of uncertain systems with time-varying delays and norm-bounded uncertainty. The stability and stabilizability of this class of systems are considered. Linear Matrix Inequalities (LMI) delay-dependent sufficient conditions for both stability and stabilizability and their robustness are established.

How to cite

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Saadni, Mohammed, and Mehdi, Driss. "Stability and stabilizability of a class of uncertain dynamical systems with delays." International Journal of Applied Mathematics and Computer Science 15.3 (2005): 321-329. <http://eudml.org/doc/207746>.

@article{Saadni2005,
abstract = {This paper deals with a class of uncertain systems with time-varying delays and norm-bounded uncertainty. The stability and stabilizability of this class of systems are considered. Linear Matrix Inequalities (LMI) delay-dependent sufficient conditions for both stability and stabilizability and their robustness are established.},
author = {Saadni, Mohammed, Mehdi, Driss},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {dynamical systems; time-varying delays; robust stabilizability; norm-bounded robust stability; time-varying uncertainty},
language = {eng},
number = {3},
pages = {321-329},
title = {Stability and stabilizability of a class of uncertain dynamical systems with delays},
url = {http://eudml.org/doc/207746},
volume = {15},
year = {2005},
}

TY - JOUR
AU - Saadni, Mohammed
AU - Mehdi, Driss
TI - Stability and stabilizability of a class of uncertain dynamical systems with delays
JO - International Journal of Applied Mathematics and Computer Science
PY - 2005
VL - 15
IS - 3
SP - 321
EP - 329
AB - This paper deals with a class of uncertain systems with time-varying delays and norm-bounded uncertainty. The stability and stabilizability of this class of systems are considered. Linear Matrix Inequalities (LMI) delay-dependent sufficient conditions for both stability and stabilizability and their robustness are established.
LA - eng
KW - dynamical systems; time-varying delays; robust stabilizability; norm-bounded robust stability; time-varying uncertainty
UR - http://eudml.org/doc/207746
ER -

References

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  1. Boukas E.-K. and Liu Z.-K. (2002): Deterministic and Stochastic Time-Delay Systems. -Boston: Birkhauser, Marcel Dekker. Zbl1052.93059
  2. de la Sen M. (2002): Stability test for two common classes of linear time-delay systems and hybrid systems. - Lutianian Math. J., Vol. 42, No. 2, pp. 153-168. Zbl1049.93074
  3. Hale J.-K. (1977): Theory of Functional Differential Equations. -New York: Springer. 
  4. Hmamed A. (1997): Further results on the robust stability of uncertain linear systems including delayed perturbations. -Automatica, Vol. 33, No. 9, pp. 1763-1765. 
  5. Kim J.-H. (2001): Delay and its time derivative dependent robust stability of time-delayed linear systems with uncertainty. -IEEETAC, Vol. 46, No. 5, pp. 789-792. Zbl1008.93056
  6. Lee B. and Lee J.-G. (1999): Robust stability and stabilization of linear delayed systems with structured uncertainty. -Automatica, Vol. 35, No. 6, pp. 1149-1154. Zbl1041.93560
  7. Lee B. and Lee J.-G. (2000): Robust control of uncertain systems with input delay and input sector nonlinearity. -Proc. 39th IEEE Conf. Decision and Control, North Sydney, Australia, Vol. 5, pp. 4430-4435. 
  8. Li X. and de Souza C.-E. (1996): Criteria for robust stability of uncertain linear systems with time-varying state delays. -Proc. 13th IFAC World Congress, San Francisco, CA, pp. 137-142. 
  9. Li X. and de Souza C.-E. (1997a): Criteria for robust stability of uncertain linear systems with state delays. - Automatica, Vol. 33, No. 9, pp. 1657-1662. 
  10. Li X. and de Souza C.-E. (1997b): Delay dependent robust stability and stabilization of uncertain linear delay systems: A linear matrix inequality approach. - IEEETAC, Vol. 42, No. 8, pp. 1144-1148. Zbl0889.93050
  11. Li X., Fu M., and de Souza C.-E. (1992): H_∞ control and quadratic stabilization of systems with parameter uncertainty via output feedback. - IEEETAC, Vol. 37, No. 8, pp. 1253-1256. Zbl0764.93067
  12. Mahmoud M.-S. (2000): Robust Control and Filtering for Time-Delay Systems. - New York: Marcel-Dekker. Zbl0969.93002
  13. Marchenko V.-M., Borkovskaja I.-M. and Jakimenko A.-A. (1996): Linear state-feedback for after-effect systems: stabilization and modal control. - Proc. 13th IFAC World Congress, San-Francisco, USA, pp. 441-446. 
  14. Niculescu S.-I., de Souza C.-E., Dion J.-M. and Dugard L. (1994): Robust stability and stabilization of uncertain linear systems with state delay: Single dealy case. - Proc. IFAC Symp. Robust Control Design, Rio de Janero, Brazil, pp. 469-474. 
  15. Su J.-H. (1994): Further results on the robust stability of linear systems with a single time-delay. - SCL, Vol. 23, pp. 375-379. Zbl0805.93045
  16. Su T.J. and Huang C.-G. (1992): Robust stability of delay dependence for linear systems. -IEEETAC, Vol. 37, No. 10, pp. 1656-1659. Zbl0770.93077
  17. Sun Y.J., Hsieh J.-G. and Yang H.-C. (1997): On the stability of uncertain systems with multiple time-varying delays. - IEEETAC, Vol. 42, No. 1, pp. 101-105. Zbl0871.93045
  18. Wang S.-S., Chen B.-S. and Lin T.-P. (1987): Robust stability of uncertain time-delay systems. -IJC, Vol. 46, No. 4, pp. 963-976. Zbl0629.93051
  19. Xu B. (1995): On delay-independent stability of large scale systems with time-delays. - IEEETAC, Vol. 40, No. 5, pp. 930-933. Zbl0825.93644
  20. Xu B. and Liu Y. (1994): An improved Razimukhin-type theorem and its applications.- IEEETAC, Vol. 39, No. 4, pp. 839-841. Zbl0807.93056

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