In discrete-time systems, instead of having a hyperplane as in the continuous case, there is a countable set of points comprising a so-called lattice; and the surface on which these sliding points lie is the latticewise hyperplane. In this paper the concept of multivariable discrete-time sliding mode is clarified and new sufficient conditions for the existence of the sliding mode are presented. A new control design using the properties of discrete sliding is proposed, and the behavior of the system in the sliding mode is studied. Furthermore, the stabilization of discrete-time systems and an optimal sliding lattice are considered. [S0022-0434(00)02804-5]
Issue Section:
Technical Papers
1.
Utkin
, V. I.
, 1977
, “Variable structure systems with sliding modes
,” IEEE Trans. Autom. Control
, 22
, pp. 212
–222
.2.
Utkin. V. I., 1992, Sliding Modes in Control and Optimization, Springer-Verlag, Berlin.
3.
Baida
, S. V.
, 1993
, “Unit sliding mode control in continuous and discrete-time systems
,” Int. J. Control
, 57
, pp. 1125
–1132
.4.
Bartolini
, G.
, Ferrara
, A.
, and Utkin
, V. I.
, 1995
, “Adaptive sliding mode control in discrete-time systems
,” Automatica
, 31
, pp. 769
–773
.5.
Chan
, C. Y.
, 1999
, “Discrete adaptive quasi-sliding mode control
,” Int. J. Control
, 72
, pp. 365
–373
.6.
Chan
, C. Y.
, 1994
, “Robust discrete-time sliding mode controller
,” Syst. and Control Lett.
, 23
, pp. 371
–374
.7.
Chen
, X.
, and Fukuda
, T.
, 1999
, “Adaptive quasi-sliding mode control for discrete-time multivariable systems
,” Int. J. Control
, 72
, pp. 133
–140
.8.
Drakunov
, S. V.
, and Utkin
, V. I.
, 1992
, “Sliding mode in dynamic systems
,” Int. J. Control
, 55
, pp. 1029
–1037
.9.
Furuta
, K.
, 1990
, “Sliding mode control of a discrete system
,” Syst. and Control. Lett.
, 14
, pp. 145
–152
.10.
Corradini
, M. L.
, and Orlando
, G.
, 1998
, “Variable structure control of discretized continuous-time systems
,” IEEE Trans. Autom. Control
, 43
, pp. 1329
–1333
.11.
Gao
, W.
, Wang
, Y.
, and Homaifa
, A.
, 1995
, “Discrete-time variable structure control
,” IEEE Trans. Ind. Electron.
, 42
, pp. 117
–122
.12.
Koshkouei, A. J., and Zinober, A. S. I., 1996, “Discrete-time sliding mode control design,” Proc. 13th IFAC Congress, Vol. G, pp. 481–486.
13.
Koshkouei, A. J., and Zinober, A. S. I., 1996, “Sliding mode state observers for SISO linear discrete-time Systems,” Proc. UKACC Int. Conference on Control’96, Exeter, pp. 837–842.
14.
Koshkouei, A. J., and Zinober, A. S. I., 1996, “Sliding lattice design for discrete-time linear multivariable systems,” Proc. 35th IEEE Conference on Decision and Control, Kobe, pp. 1497–1502.
15.
Kotta
, U.
, 1989
, “Comments on ‘On the stability of discrete-time sliding mode control systems’
,” IEEE Trans. Autom. Control
, 34
, pp. 1021
–1022
.16.
Milosavljevic´
, C.
, 1985
, “General conditions for the existence of a quasisliding on the switching hyperplane in discrete variable structure systems
,” Automat. Remote Control
, 46
, pp. 307
–314
.17.
Sarpturk
, S. Z.
, Istefanopulos
, Y.
, and Kaynak
, O.
, 1987
, “On the stability of discrete-time sliding mode control systems
,” IEEE Trans. Autom. Control
, 32
, pp. 930
–932
.18.
Sira-Ramı´rez
, H.
, 1991
, “Non-linear discrete variable structure systems in quasi-sliding mode
,” Int. J. Control
, 54
, pp. 1171
–1187
.19.
Spurgeon, S. K., 1991, “Sliding mode control design for uncertain discrete-time systems,” Proc. 30th IEEE Conference on Decision and Control, Brighton, pp. 2136–2141.
20.
Spurgeon
, S. K.
, 1992
, “Hyperplane design techniques for discrete-time variable structure control systems
,” Int. J. Control
, 55
, pp. 445
–456
.21.
Su, W.-C., Drakunov, S. V., Ozgu¨ner, U¨., and Redmill, K., 1995, “OT2 sliding mode control on a flexible structure,” Proc. Amer. Control Conference, Seattle, pp. 1318–1322.
22.
Utkin, V. I., 1994, “Sliding mode control in discrete-time and difference systems,” Variable Structure and Lyapunov Control, Zinober, A. S. I., ed., Springer-Verlag, Berlin.
23.
Yu, X., 1994, “Digital variable structure control with the pseudo-sliding modes,” Variable Structure and Lyapunov Control, Zinober, A. S. I., ed., Springer-Verlag, Berlin.
24.
Yu
, X.
, and Potts
, R. B.
, 1992
, “Analysis of discrete-time variable structure systems with pseudo-sliding modes
,” Int. J. Syst. Sci.
, 23
, pp. 503
–516
.25.
Magan˜a
, M. E.
, and Z˙ak
, S. H.
, 1988
, “Robust state feedback stabilization of discrete-time uncertain dynamical systems
,” IEEE Trans. Autom. Control
, 33
, pp. 887
–891
.26.
Corless, M., and Manela, J., 1986, “Control of uncertain discrete-time systems,” Proc. Amer. Control Conference, Seattle, pp. 515–520.
27.
Sezer
, M. E.
, and Sˇiljak
, D. D.
, 1988
, “Robust stability of discrete systems
,” Int. J. Control
, 48
, pp. 2055
–2063
.28.
Yaz
, E.
, and Niu
, X.
, 1989
, “Stability robustness of discrete-time systems in the presence of uncertainty
,” Int. J. Control
, 50
, pp. 173
–182
.29.
Yaz
, E.
, 1991
, “Robustness of discrete-time systems for unstructured stochastic perturbations
,” IEEE Trans. Autom. Control
, 36
, pp. 867
–869
.30.
Barnett, S., 1983, Polynomials and Linear Control Systems, Marcel Dekker, New York.
31.
Ogata, K., 1995, Discrete-Time Control Systems, Prentice-Hall, New Jersey.
32.
Furuta
, K.
, and Kim
, B. S.
, 1987
, “Pole assignment in a specified disk
,” IEEE Trans. Autom. Control
, 32
, pp. 423
–427
.33.
Young
, K. D.
, Kokotovic´
, P. V.
, and Utkin
, V. I.
, 1977
, “A singular perturbation analysis of high-gain feedback systems
,” IEEE Trans. Autom. Control
, 22
, pp. 931
–937
.34.
Wang
, W.-J.
, Wu
, G.-H.
, and Yang
, D.-C.
, 1994
, “Variable structure control design for uncertain discrete-time systems
,” IEEE Trans. Autom. Control
, 39
, pp. 99
–102
.35.
Myszkorowski
, P.
, and Holmberg
, U.
, 1994
, “Comments on ‘Variable structure control design for uncertain discrete-time systems’
,” IEEE Trans. Autom. Control
, 39
, pp. 2366
–2367
.Copyright © 2000
by ASME
You do not currently have access to this content.
