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Sliding mode controller-observer design for multivariable linear systems with unmatched uncertainty
Kybernetika, Tome 36 (2000) no. 1, pp. 95-115 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 93B12, 93B51, 93C10, 93C35, 93D20
Keywords: sliding mode control; multivariable linear systems; uncertainty 
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Koshkouei, A. Jafari; Zinober, Alan S. I. Sliding mode controller-observer design for multivariable linear systems with unmatched uncertainty. Kybernetika, Tome 36 (2000) no. 1, pp. 95-115. http://geodesic.mathdoc.fr/item/KYB_2000_36_1_a8/

[1] Dorling C. M., Zinober A. S. I.: A comparative study of the sensitivity of observers. In: Proc. First IASTED Symposium on Applied Control and Identification, Copenhagen 1983, pp. 6.32–6.37

[2] Dorling C. M., Zinober A. S. I.: Two approaches to hyperplane design in multivariable variable structure control systems. Internat. J. Control 44 (1986), 65–82 | DOI | Zbl

[3] Draženović B.: The invariance condition in variable structure systems. Automatica 5 (1969), 287–295 | DOI | MR

[4] Edwards C., Spurgeon S. K.: On the development of discontinuous observers. Internat. J. Control 59 (1994), 1211–1229 | DOI | MR | Zbl

[5] El-Ghezawi O. M. E., Zinober A. S. I., Billings S. A.: Analysis and design of variable structure systems using a geometric approach. Internat. J. Control 38 (1983), 657–671 | DOI | MR | Zbl

[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

[7] Koshkouei A. J., Zinober A. S. I.: Sliding mode controller-observer design for SISO linear systems. Internat. J. Systems Sci. 12 (1998), 1363–1373 | DOI | Zbl

[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

[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

[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

[11] Sira-Ramírez H., Spurgeon S. K.: On the robust design of sliding mode observers for linear systems. Systems Control Lett. 23 (1994), 9–14 | DOI | MR

[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

[13] Utkin V. I.: Sliding Modes in Control and Optimization. Springer–Verlag, Berlin 1992 | MR | Zbl

[14] Walcott B. L., Żak S. H.: State observation of nonlinear uncertain dynamical systems. IEEE Trans. Automat. Control 32 (1987), 166–170 | DOI | MR | Zbl