Sliding mode control in the presence of delay

Jean-Pierre Richard; Fréderic Gouaisbaut; Wilfrid Perruquetti

Kybernetika (2001)

  • Volume: 37, Issue: 3, page [277]-294
  • ISSN: 0023-5954

Abstract

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This paper provides an overview of recent results for relay-delay systems. In a first section, simple examples illustrate the problems induced by delays in the synthesis of sliding mode controllers. Then, a brief overview of the existing results shows the present advances and limits in this domain. The last parts of the paper are devoted to new results: first, for systems with state delay, then for systems with input delay.

How to cite

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Richard, Jean-Pierre, Gouaisbaut, Fréderic, and Perruquetti, Wilfrid. "Sliding mode control in the presence of delay." Kybernetika 37.3 (2001): [277]-294. <http://eudml.org/doc/33535>.

@article{Richard2001,
abstract = {This paper provides an overview of recent results for relay-delay systems. In a first section, simple examples illustrate the problems induced by delays in the synthesis of sliding mode controllers. Then, a brief overview of the existing results shows the present advances and limits in this domain. The last parts of the paper are devoted to new results: first, for systems with state delay, then for systems with input delay.},
author = {Richard, Jean-Pierre, Gouaisbaut, Fréderic, Perruquetti, Wilfrid},
journal = {Kybernetika},
keywords = {relay-delay system; sliding mode controllers; input delay; state delay; relay-delay system; sliding mode controllers; input delay; state delay},
language = {eng},
number = {3},
pages = {[277]-294},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Sliding mode control in the presence of delay},
url = {http://eudml.org/doc/33535},
volume = {37},
year = {2001},
}

TY - JOUR
AU - Richard, Jean-Pierre
AU - Gouaisbaut, Fréderic
AU - Perruquetti, Wilfrid
TI - Sliding mode control in the presence of delay
JO - Kybernetika
PY - 2001
PB - Institute of Information Theory and Automation AS CR
VL - 37
IS - 3
SP - [277]
EP - 294
AB - This paper provides an overview of recent results for relay-delay systems. In a first section, simple examples illustrate the problems induced by delays in the synthesis of sliding mode controllers. Then, a brief overview of the existing results shows the present advances and limits in this domain. The last parts of the paper are devoted to new results: first, for systems with state delay, then for systems with input delay.
LA - eng
KW - relay-delay system; sliding mode controllers; input delay; state delay; relay-delay system; sliding mode controllers; input delay; state delay
UR - http://eudml.org/doc/33535
ER -

References

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  1. Aggoune W., Contribution à la Stabilisation de Systèmes Non Linéaires: Application Aux Systèmes Non Réguliers et Aux Systèmes à Retards, (In French.) INRIA Lorraine/CRAN, University of Metz 1999 
  2. Bonnet C., Partington, J., Sorine M., Robust control and tracking in l ∞ of delay systems equipped with a relay sensor, In: LSS’98, 8th IFAC Conference Large Scale Systems, Patras 1998 
  3. Cheres E., Gutman, S., Palmor Z., 10.1109/9.40753, IEEE Trans. Automat. Control 34 (1989), 11, 1199–1203 (1989) Zbl0693.93059MR1020938DOI10.1109/9.40753
  4. Choi H., An LMI approach to sliding mode control design for a class of uncertain time delay systems, In: European Control Conference ECC’99, Karlsruhe 1999 
  5. Choi S., Hedrick J., 10.1109/87.668034, IEEE Trans. Control Syst. Technology 6 (1998), 3, 325–334 (1998) DOI10.1109/87.668034
  6. Dambrine M., Gouaisbaut F., Perruquetti, W., Richard J.-P., Robustness of sliding mode control under delays effects: a case study, In: Proc. 2nd IEEE-IMACS CESA’98, Comput. Eng. in Systems Applications, Hamamet 1998, pp. 817–821 (1998) 
  7. Carlo R. De, Zak, S., Matthews G., Variable structure control of nonlinear variable systems: A tutorial, Proc. IEEE 76 (1988), 212–232 (1988) 
  8. Dugard L., Verriest E. I., Stability and Control of Time-Delay Systems, (Lecture Notes in Control and Information Sciences 228.) Springer Verlag, Berlin 1997 Zbl0901.00019MR1482570
  9. El–Khazaly R., 10.1016/S0005-1098(97)00200-8, Automatica 34 (1998), 3, 327–332 (1998) MR1623124DOI10.1016/S0005-1098(97)00200-8
  10. Fiagbedzi Y., Pearson A., 10.1109/TAC.1986.1104417, IEEE Trans. Automat. Control 31 (1986), 847–855 (1986) Zbl0601.93045MR0853435DOI10.1109/TAC.1986.1104417
  11. Fliess M., Generalized controller canonical forms for linear and nonlinear dynamics, IEEE Trans. Autémat. Control 35 (1990), 9, 994–1000 (1990) Zbl0724.93010MR1065035
  12. Fridman L., Fridman, E., Shustin E., Steady modes in an autonomous system with break and delay, J. Differential Equations 29 (1993), 8 (1993) Zbl0808.34076
  13. Fridman L., Fridman, E., Shustin E., Steady modes and sliding modes in the relay control systems with time delay, In: 35th IEEE CDC’96 (Conference on Decision and Control), Kobe 1996, pp. 4601–4606 (1996) 
  14. Gouaisbaut F., Blanco, Y., Richard J., Robust control of nonlinear time delay system: A sliding mode control design, In: IFAC Symposium NOLCOS’01, St Petersburg 2001. Accepted 
  15. Gouaisbaut F., Dambrine, M., Richard J.-P., Sliding mode control of perturbed systems with time varying delays, In: SCS’01, IFAC Symposium on Structure and Control Systems, Prague 2001 
  16. Gouaisbaut F., Perruquetti W., Orlov, Y., Richard J.-P., A sliding mode controller for linear time delay systems, In: Proc. ECC’99 European Control Conference, Karlsruhe 1999 
  17. Gouaisbaut F., Perruquetti W., Richard J.-P., A sliding mode control for linear systems with input and state delays, In: Proc. CDC’99, 38th Conference on Decision and Control, Phoenix 1999 
  18. Goubet–Bartholoméüs A., Dambrine, M., Richard J.-P., 10.1016/S0167-6911(97)00032-7, Systems Control Lett. 31 (1997), 155–163 (1997) MR1470693DOI10.1016/S0167-6911(97)00032-7
  19. Kolmanovskii V., Myshkis A., Applied Theory of Functional Differential Equations (Math, Appl. 85.) Kluwer, Dordrecht 1992 MR1256486
  20. Kolmanovskii V., Myshkis A., Introduction to the Theory and Applications of Functional Differential Equations, Kluwer, Dordrecht 1999 Zbl0917.34001MR1680144
  21. Kolmanovskii V., Niculescu, S., Richard J.-P., 10.1080/002071799221172, Internat. J. Control 72 (1999), 4, 374–384 (1999) MR1675003DOI10.1080/002071799221172
  22. Kolmanovskii V., Richard J.-P., 10.1109/9.763213, IEEE Trans. Automat. Control 44 (1999), 5, 984–989 (1999) MR1690541DOI10.1109/9.763213
  23. Li X., Yurkovich S., Sliding mode control of systems with delayed states and control, Variable Structure Systems, Sliding Mode and Nonlinear Control 247 (1999), 1 (1999) MR1714565
  24. Lukyanov A., Utkin V., Methods of reducing equations of dynamics systems to regular form, Automat. Remote Control 42 (1981), 413–420 (1981) 
  25. Luo N., Sen M. De la, State feedback sliding mode controls of a class of time-delay systems, In: ACC’92 (American Control Conference), Chicago 1992, pp. 894–895 (1992) 
  26. Luo N., Sen M. De la, 10.1049/ip-d.1993.0035, IEE Proceedings-D 140 (1993), 4, 261–274 (1993) DOI10.1049/ip-d.1993.0035
  27. Manitius A., Olbrot A., 10.1109/TAC.1979.1102124, IEEE Trans. Automat. Control 24 (1979), 4, 541–553 (1979) Zbl0425.93029MR0538808DOI10.1109/TAC.1979.1102124
  28. Orlov Y., 10.1109/9.855545, IEEE Trans. Automat. Control 45 (2000), 5, 834–843 Zbl0973.93018MR1774140DOI10.1109/9.855545
  29. Orlov Y., Utkin V., 10.1016/0005-1098(87)90032-X, Automatica 6 (1987), 753–757 (1987) Zbl0661.93036MR0922555DOI10.1016/0005-1098(87)90032-X
  30. Perruquetti W., Barbot J., Sliding Mode Control in Engineering, Marcel Dekker, New York 2001. To appear 
  31. Richard J., Some trends and tools for the study of time delay systems, In: 2nd Conference IMACS-IEEE CESA’98, Computational Engineering in Systems Applications, Tunisia 1998, pp. 27–43 (1998) 
  32. Richard J., Kolmanovskii V. E., Delay systems, Mathematics and Computers in Simulation (Special issue), 45 (1998), 3–4 (1998) Zbl1017.93507MR1622951
  33. Roh Y., Oh J., Robust stabilization of uncertain input-delay systems by sliding mode control with delay compensation, Automatica 35 (1999), 1681–1685 (1999) Zbl0931.93015MR1831769
  34. Shyu K., Yan J., 10.1080/00207179308934385, Internat. J. Control 57 (1993), 237–246 (1993) Zbl0774.93066MR1201742DOI10.1080/00207179308934385
  35. Sira–Ramirez H., 10.1080/00207178808906256, Internat. J. Control 48 (1998), 4, 1359–1390 (1998) MR0964768DOI10.1080/00207178808906256
  36. Tan K., Wang, Q., Lee T., 10.1021/ie970765o, Ind. Eng. Chem. Res. 37 (1998), 4, 1351–1357 (1998) DOI10.1021/ie970765o
  37. Utkin V., Sliding Modes in Control Optimization, CCES Springer–Verlag, Berlin 1991 MR1295845
  38. Zheng F., Cheng, M., Gao W.-B., 10.1016/0005-1098(95)00012-L, Automatica 31 (1995), 7, 1031–1037 (1995) Zbl0842.93011MR1343573DOI10.1016/0005-1098(95)00012-L

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