New trends in design of observers for time-delay systems

Olivier Sename

Kybernetika (2001)

  • Volume: 37, Issue: 4, page [427]-458
  • ISSN: 0023-5954

Abstract

top
This paper presents some recent results about the design of observers for time-delay systems. It is focused on methods that can lead to design some useful observers in practical situations. First the links between observability properties and observers design is emphasized. Then some necessary and sufficient conditions and a method are provided to obtain unknown input observers for time-delay systems. Furthermore some H design using Lyapunov–Krasovskii and Lyapunov–Razumikhin theories are presented and compared. Finally a polynomial approach based on the parametrization of all observers is proposed that allows to design robust observers for systems including unstructured uncertainties.

How to cite

top

Sename, Olivier. "New trends in design of observers for time-delay systems." Kybernetika 37.4 (2001): [427]-458. <http://eudml.org/doc/33545>.

@article{Sename2001,
abstract = {This paper presents some recent results about the design of observers for time-delay systems. It is focused on methods that can lead to design some useful observers in practical situations. First the links between observability properties and observers design is emphasized. Then some necessary and sufficient conditions and a method are provided to obtain unknown input observers for time-delay systems. Furthermore some $H_\{\infty \}$ design using Lyapunov–Krasovskii and Lyapunov–Razumikhin theories are presented and compared. Finally a polynomial approach based on the parametrization of all observers is proposed that allows to design robust observers for systems including unstructured uncertainties.},
author = {Sename, Olivier},
journal = {Kybernetika},
keywords = {time-delay system; observability; time-delay system; observability},
language = {eng},
number = {4},
pages = {[427]-458},
publisher = {Institute of Information Theory and Automation AS CR},
title = {New trends in design of observers for time-delay systems},
url = {http://eudml.org/doc/33545},
volume = {37},
year = {2001},
}

TY - JOUR
AU - Sename, Olivier
TI - New trends in design of observers for time-delay systems
JO - Kybernetika
PY - 2001
PB - Institute of Information Theory and Automation AS CR
VL - 37
IS - 4
SP - [427]
EP - 458
AB - This paper presents some recent results about the design of observers for time-delay systems. It is focused on methods that can lead to design some useful observers in practical situations. First the links between observability properties and observers design is emphasized. Then some necessary and sufficient conditions and a method are provided to obtain unknown input observers for time-delay systems. Furthermore some $H_{\infty }$ design using Lyapunov–Krasovskii and Lyapunov–Razumikhin theories are presented and compared. Finally a polynomial approach based on the parametrization of all observers is proposed that allows to design robust observers for systems including unstructured uncertainties.
LA - eng
KW - time-delay system; observability; time-delay system; observability
UR - http://eudml.org/doc/33545
ER -

References

top
  1. Chen J., Patton R. J., Robust model-based fault diagnosis for dynamic systems, Kluwer Academic Publishers, Dordrecht 1999 Zbl0920.93001
  2. Choi H. H., Chung M. J., 10.1016/0005-1098(96)00014-3, Automatica 32 (1996), 7, 1073–1075 (1996) MR1405466DOI10.1016/0005-1098(96)00014-3
  3. Choi H. H., Chung M. J., Robust observer-based H controller design for linear uncertain time-delay systems, Automatica 33 (1997), 9, 1749–1752 (1997) MR1481837
  4. Darouach M., Zasadzinski, M., Xu S. J., 10.1109/9.280770, IEEE Trans. Automat. Control 39 (1994), 3, 606–609 (1994) Zbl0813.93015MR1268304DOI10.1109/9.280770
  5. DeSouza C. E., Palhares R. M., Peres P. L. D., Robust H filtering for uncertain linear systems with multiple time-varying state delays: An LMI approach, In: Proc. 38th IEEE Conference on Decision and Control, Phoenix 1999, pp. 2023–2028 (1999) 
  6. Dugard L., (eds) E. I. Verriest, Stability and Control of Time-delay Systems, (Lecture Notes in Control and Inform. Sci. 228.) Springer Verlag, Berlin 1998 MR1482570
  7. Eising R., 10.1016/0167-6911(82)90006-8, Systems Control Lett. 2 (1982), 1, 225–229 (1982) Zbl0519.93033MR0690234DOI10.1016/0167-6911(82)90006-8
  8. Emre E., Khargonekar P. P., 10.1109/TAC.1982.1102815, IEEE Trans. Automat. Control 27 (1982), 1, 104–113 (1982) Zbl0502.93019MR0673076DOI10.1109/TAC.1982.1102815
  9. Fattouh A., Robust Observation and Digital Control for Systems with Time-delays (in French), Ph. D. Thesis, I.N.P.G – Laboratoire d’Automatique de Grenoble, Grenoble 2000 
  10. Fattouh A., Sename, O., Dion J.–M., H observer design for time-delay systems, In: Proc. 37th IEEE Conference on Decision and Control, Tampa 1998, pp. 4545–4546 (1998) 
  11. Fattouh A., Sename, O., Dion J.–M., Robust observer design for time-delay systems: A Riccati equation approach, Kybernetika 35 (1999), 6, 753–764 (1999) MR1747974
  12. Fattouh A., Sename, O., Dion J.–M., An unknown input observer design for linear time-delay systems, In: Proc. 38th IEEE Conference on Decision and Control, Phoenix 1999, pp. 4222–4227 (1999) 
  13. Fattouh A., Sename, O., Dion J.–M., H controller and observer design for linear systems with point and distributed time-delays: An LMI approach, In: 2nd IFAC Workshop on Linear Time Delay Systems, Ancône 2000 
  14. Fattouh A., Sename, O., Dion J.–M., An LMI approach to robust observer design for linear time-delay systems, In: Proc. 39th IEEE Conference on Decision and Control, Sydney 2000 
  15. Fattouh A., Sename, O., Dion J.–M., Robust observer design for linear uncertain time-delay systems: A factorization approach, In: 14th Internat. Symposium on Mathematical Theory of Networks and Systems, Perpignan 2000 
  16. Fiagbedzi Y. A., Pearson A. E., 10.1080/00207179008934056, Internat. J. Control 51 (1990), 1, 189–204 (1990) Zbl0695.93086MR1035873DOI10.1080/00207179008934056
  17. Habets L., Algebraic and Computational Aspects of Time-delay Systems, Ph. D. Thesis, Eindhoven University of Technology 1994 Zbl0804.93031MR1276720
  18. Hou M., Müller P. C., 10.1109/9.256351, IEEE Trans. Automat. Control 37 (1992), 6, 871–875 (1992) Zbl0775.93021MR1164570DOI10.1109/9.256351
  19. Ivanescu D., Snyder A. F., Dion J.–M., Dugard L., Georges, D., Hadjsaid N., Robust stabilizing controller for an interconnected power system: A time delay approach, In: 14th Internat. Symposium on Mathematical Theory of Networks and Systems, Perpignan 2000 
  20. Jankovic M., Kolmanovsky I., Controlling nonlinear systems through time-delays: an automotive perspective, In: Proc. 8th European Control Conference ECC’99, Karlsruhe 1999 
  21. Kamen E. W., Khargonekar P. P., Tannenbaum A., 10.1080/00207178608933506, Internat. J. Control 43 (1986), 3, 837–857 (1986) Zbl0599.93047MR0828360DOI10.1080/00207178608933506
  22. Kučera V., Discrete Linear Control: The Polynomial Equation Approach, Wiley, Chichester 1979 Zbl0432.93001MR0573447
  23. Lee E.B., Lu W. S., Coefficient assignability for linear systems with delays, IEEE Trans. Automat. Control AC-29 (1984), 128–131 (1984) Zbl0561.93025MR0764706
  24. Lee E. B., Olbrot A. W., 10.1080/00207178108922582, Internat. J. Control 34 (1981), 1061–1078 (1981) Zbl0531.93015MR0643872DOI10.1080/00207178108922582
  25. Lee E. B., Zak S. H., 10.1109/TAC.1982.1102931, IEEE Trans. Automat. Control AC-27 (1982), 446–449 (1982) Zbl0492.93019MR0680110DOI10.1109/TAC.1982.1102931
  26. Lee J. H., Kim S. W., Kwon W. H., 10.1109/9.273356, IEEE Trans. Automat. Control 39 (1994), 1, 159–162 (1994) MR1258692DOI10.1109/9.273356
  27. Manitius A., Triggiani R., 10.1137/0316041, SIAM J. Control Optim. 16 (1978), 4, 599–645 (1978) Zbl0442.93009MR0482505DOI10.1137/0316041
  28. Morse A. S., 10.1016/0005-1098(76)90013-3, Automatica 12 (1976), 529–531 (1976) Zbl0345.93023MR0437162DOI10.1016/0005-1098(76)90013-3
  29. Niculescu S. I., On the stability and stabilization of linear systems with delayed-state (in French), Ph. D. Thesis, Laboratoire d’Automatique de Grenoble, INPG, 1996 
  30. Niculescu S. I., Trofino–Neto A., Dion, J.–M., Dugard L., Delay-dependent stability of linear systems with delayed state: An l, m.i. approach. In: Proc. 34th Conference on Decision and Control, New Orleans 1995, pp. 1495–1496 (1995) 
  31. Nobuyama E., Kitamori T., Spectrum assignment and parameterization of all stabilizing compensators for time-delay systems, In: Proc. 29th Conference on Decision and Control, Honolulu 1990, pp. 3629–3634 (1990) 
  32. Pearson A. E., Fiagbedzi Y. A., 10.1109/9.29412, IEEE Trans. Automat. Control 34 (1989), 7, 775–777 (1989) Zbl0687.93011MR1000675DOI10.1109/9.29412
  33. Picard P., Lafay J. F., Kučera V., 10.1109/9.587342, IEEE Trans. Automat. Control 42 (1997), 6, 848–852 (1997) Zbl0888.93029MR1455716DOI10.1109/9.587342
  34. Picard P., Sename, O., Lafay J. F., Observers and observability indices for linear systems with delays, In: CESA 96, IEEE Conference on Computational Engineering in Systems Applications, volume 1, Lille 1996, pp. 81–86 (1996) 
  35. Pourboghrat F., Chyung D. H., 10.1080/00207178608933637, Internat. J. Control 44 (1986), 3, 867–877 (1986) Zbl0603.93008MR0850351DOI10.1080/00207178608933637
  36. Richard S., Chevrel, P., Maillard B., Active control of future vehicle drivelines, In: Proc. 38th IEEE Conference on Decision and Control, Phoenix 1999, pp. 3752–3767 (1999) 
  37. Salamon D., 10.1109/TAC.1980.1102507, IEEE Trans. Automat. Control 25 (1980), 6, 1187–1192 (1980) Zbl0471.93011MR0601503DOI10.1109/TAC.1980.1102507
  38. Sename O., Unknown input robust observers for time-delay systems, In: 36th IEEE Conference on Decision and Control, San Diego 1997, pp. 1629–1630 (1997) 
  39. Sename O., Lafay J. F., Rabah R., Controllability indices of linear systems with delays, Kybernetika 6 (1995), 559–580 (1995) Zbl0864.93023MR1374145
  40. Sontag E. D., Linear systems over commutative rings; a survey, Ricerche Automat. 7 (1976), 1–16 (1976) 
  41. Su J.-H., 10.1016/0167-6911(94)90071-X, Systems Control Lett. 23 (1994), 375–379 (1994) Zbl0805.93045MR1303587DOI10.1016/0167-6911(94)90071-X
  42. Tornambè A., 10.1080/00207729208949399, Internat. J. Systems Sci. 23 (1992), 9, 1463–1473 (1992) Zbl0781.93045MR1181805DOI10.1080/00207729208949399
  43. Wang Z., Huang, B., Unbehauen H., Robust H observer design for uncertain time-delay systems: (i) the continuous-time case, In: IFAC 14th World Congress, Beijing 1999, pp. 231–236 (1999) 
  44. Watanabe K., 10.1109/TAC.1986.1104336, IEEE Trans. Automat. Control AC-31 (1986), 6, 543–550 (1986) Zbl0596.93009MR0839083DOI10.1109/TAC.1986.1104336
  45. Watanabe K., Ouchi T., 10.1080/0020718508961121, Internat. J. Control 41 (1985), 1, 217–229 (1985) MR0775229DOI10.1080/0020718508961121
  46. Wonham W. M., Linear Multivariable Control: A Geometric Approach, Springer Verlag, New York 1979 Zbl0609.93001MR0569358
  47. Yao Y. X., Zhang Y. M., Kovacevic R., Parameterization of observers for time delay systems and its application in observer design, IEE Proc. – Control Theory Appl. 143 (1996), 3, 225–232 (1996) 
  48. Yao Y. X., Zhang Y. M., Kovacevic R., 10.1080/002071797224612, Internat. J. Control 66 (1997), 4, 603–617 (1997) Zbl0873.93015MR1673792DOI10.1080/002071797224612

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.