In this paper, the tracking problem for a class of uncertain nonlinear systems with time-varying delay arguments and deadzone nonlinearities is considered. A feedback control is proposed such that the states of the feedback-controlled system track the desired trajectories with any prespecified exponential rate of convergence. A numerical example is provided to illustrate the use of our main result.

1.
Anderson, P. M., and Fouad, A. A., Power System Control and Stability, Iowa State Univ. Press, Ames, IA, 1982.
2.
Burton, T. A., Stability and Periodic Solutions of Ordinary and Functional Differential Equations, Academic Press, Orlando, 1985.
3.
Chern
T. L.
, and
Wu
Y. C.
, “
Design of Integral Variable Structure Controller and Application to Electrohydraulic Velocity Servosystems
,”
IEE Proceedings Part D
, Vol.
138
,
1991
, pp.
439
444
.
4.
Chern
T. L.
, and
Wu
Y. C.
, “
Integral Variable Structure Control Approach for Robot Manipulators
,”
IEE Proceedings Part D
, Vol.
139
,
1992
, pp.
161
166
.
5.
Chern
T. L.
, and
Wu
Y. C.
, “
An Optimal Variable Structure Control with Integral Compensation for Electrohydraulic Position Servo Control Systems
,”
IEEE Transactions on Industry Electronics
, Vol.
39
,
1992
, pp.
460
463
.
6.
Chern
T. L.
, and
Wu
Y. C.
, “
Design of Brushless DC Position Servo Systems Using Integral Variable Structure Approach
,”
IEE Proceedings Part D
, Vol.
140
,
1993
, pp.
27
34
.
7.
Chyung, D. H., “Robust Tracking Controller for Time Delay Systems,” Proceedings of the 28th Conference on Decision and Control, Tampa, FL, 1989.
8.
Chyung, D. H., “Feedforward Tracking Controller for Systems Containing Time Delays,” Proceedings of the 1990 American Control Conference, San Diego, CA, 1990.
9.
Chyung
D. H.
, “
Tracking Controller for Linear Systems with Time Delays in Both State and Control Variables
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
115
,
1993
, pp.
179
183
.
10.
Chyung, D. H., “Tracking Controller for Output Feedback Linear Time Delay Systems,” Proceedings of the 1993 American Control Conference, San Francisco, CA, 1993.
11.
Corless
M. J.
, and
Leitmann
G.
, “
Continuous State Feedback Guaranteeing Uniform Ultimate Boundedness for Uncertain Dynamic Systems
,”
IEEE Transactions on Automatic Control
, Vol.
26
,
1981
, pp.
1139
1141
.
12.
Hale, J. K., Theory of Functional Differential Equations, Springer-Verlag, New York, 1977.
13.
Khalil, H. K., Nonlinear Systems, Macmillan, New York, 1992.
14.
Kolmanovskii, V. B., and Nosov, V. R., Stability of Functional Differential Equations, Academic Press, London, 1986.
15.
Recker, D. A., Kokotovic, P. V., Rhode, D., and Winkelman, J., “Adaptive Nonlinear Control of Systems Containing a Deadzone,” Proceedings of the 30th Conference on Decision and Control, Brighton, England, 1991.
16.
Tao
G.
, and
Kokotovic
P. V.
, “
Adaptive Control of Plants with Unknown Deadzones
,”
IEEE Transactions on Automatic Control
, Vol.
39
,
1994
, pp.
59
68
.
17.
Tao
G.
, and
Kokotovic
P. V.
, “
Adaptive Control of Partially Known Systems
,”
IEEE Transactions on Automatic Control
, Vol.
40
,
1994
, pp.
1813
1818
.
18.
Thaler, G. J., and Pastel, M. P., Analysis and Design of Nonlinear Feedback Control Systems, McGraw-Hill, New York, 1962.
19.
Zinober, A. S. I., Variable Structure and Lyapunov Control, Springer-Verlag, London, 1993.
This content is only available via PDF.
You do not currently have access to this content.