Sliding mode controller-observer design for multivariable linear systems with unmatched uncertainty

A. Jafari Koshkouei; Alan S. I. Zinober

Kybernetika (2000)

  • Volume: 36, Issue: 1, page [95]-115
  • ISSN: 0023-5954

Abstract

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This paper presents sufficient conditions for the sliding mode control of a system with disturbance input. The behaviour of the sliding dynamics in the presence of unmatched uncertainty is also studied. When a certain sufficient condition on the gain feedback matrix of the discontinuous controller and the disturbance bound holds, then the disturbance does not affect the sliding system. The design of asymptotically stable sliding observers for linear multivariable systems is presented. A sliding observer design ensures that in the presence of unmatched uncertainty, the estimated state nearly approaches the actual state. The error of the approximation depends upon the distance and bound of the unmatched uncertainty. However, certain sufficient conditions should be satisfied for the asymptotic stability of the error system.

How to cite

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Koshkouei, A. Jafari, and Zinober, Alan S. I.. "Sliding mode controller-observer design for multivariable linear systems with unmatched uncertainty." Kybernetika 36.1 (2000): [95]-115. <http://eudml.org/doc/33472>.

@article{Koshkouei2000,
abstract = {This paper presents sufficient conditions for the sliding mode control of a system with disturbance input. The behaviour of the sliding dynamics in the presence of unmatched uncertainty is also studied. When a certain sufficient condition on the gain feedback matrix of the discontinuous controller and the disturbance bound holds, then the disturbance does not affect the sliding system. The design of asymptotically stable sliding observers for linear multivariable systems is presented. A sliding observer design ensures that in the presence of unmatched uncertainty, the estimated state nearly approaches the actual state. The error of the approximation depends upon the distance and bound of the unmatched uncertainty. However, certain sufficient conditions should be satisfied for the asymptotic stability of the error system.},
author = {Koshkouei, A. Jafari, Zinober, Alan S. I.},
journal = {Kybernetika},
keywords = {sliding mode control; multivariable linear systems; uncertainty; sliding mode control; multivariable linear systems; uncertainty},
language = {eng},
number = {1},
pages = {[95]-115},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Sliding mode controller-observer design for multivariable linear systems with unmatched uncertainty},
url = {http://eudml.org/doc/33472},
volume = {36},
year = {2000},
}

TY - JOUR
AU - Koshkouei, A. Jafari
AU - Zinober, Alan S. I.
TI - Sliding mode controller-observer design for multivariable linear systems with unmatched uncertainty
JO - Kybernetika
PY - 2000
PB - Institute of Information Theory and Automation AS CR
VL - 36
IS - 1
SP - [95]
EP - 115
AB - This paper presents sufficient conditions for the sliding mode control of a system with disturbance input. The behaviour of the sliding dynamics in the presence of unmatched uncertainty is also studied. When a certain sufficient condition on the gain feedback matrix of the discontinuous controller and the disturbance bound holds, then the disturbance does not affect the sliding system. The design of asymptotically stable sliding observers for linear multivariable systems is presented. A sliding observer design ensures that in the presence of unmatched uncertainty, the estimated state nearly approaches the actual state. The error of the approximation depends upon the distance and bound of the unmatched uncertainty. However, certain sufficient conditions should be satisfied for the asymptotic stability of the error system.
LA - eng
KW - sliding mode control; multivariable linear systems; uncertainty; sliding mode control; multivariable linear systems; uncertainty
UR - http://eudml.org/doc/33472
ER -

References

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  6. Koshkouei A. J., Zinober A. S. I., Sliding mode state observers for multivariable systems, In: Proc. 34th IEEE Conference Decision and Control, 1995, pp. 2115–2120 (1995) 
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  8. Koshkouei A. J., Zinober A. S. I., Multivariable sliding mode observer design for linear systems with unmatched uncertainty, In: Proc. IEEE Mediterranean Conference on Control and Systems, Sardinia 1998, pp. 113–118 (1998) 
  9. Koshkouei A. J., Zinober A. S. I., Sliding mode observer design in the presence of unmatched uncertainty, In: Proc. IEEE VSS98 Conference, Florida 1998, pp. 96–102 (1998) 
  10. Koshkouei A. J., Zinober A. S. I., Sliding mode controller–observer design for MIMO linear systems, In: IEEE VSS98 Conference, Florida 1998, pp. 195–201 (1998) 
  11. Sira-Ramírez H., Spurgeon S. K., 10.1016/0167-6911(94)90076-0, Systems Control Lett. 23 (1994), 9–14 (1994) MR1287593DOI10.1016/0167-6911(94)90076-0
  12. Thein M.-W., Misawa E. A., Comparison of the sliding observer to several state estimators using a rotational inverted pendulum, In: Proc. 34th IEEE Conference Decision and Control, New Orleans 1995, pp. 3385–3390 (1995) 
  13. Utkin V. I., Sliding Modes in Control and Optimization, Springer–Verlag, Berlin 1992 Zbl0748.93044MR1295845
  14. Walcott B. L., Żak S. H., 10.1109/TAC.1987.1104530, IEEE Trans. Automat. Control 32 (1987), 166–170 (1987) Zbl0618.93019MR0872591DOI10.1109/TAC.1987.1104530

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