In this paper, the robust stability problem for a class of nominally stable uncertain discrete singularly perturbed linear systems with multiple time delays is considered. A stability criterion for the slow and fast subsystems is first derived. A delay-dependent criterion is then proposed to guarantee the robust stability of the system subject to norm-bounded perturbations. A numerical example is provided to illustrate our main results.
Issue Section:
Technical Briefs
1.
Gorecki, H., Fuksa, S., Grabowski, P., and Korytowski, A. 1989, Analysis and Synthesis of Time Delay Systems, Wiley, Chichester.
2.
Trinh
, H.
, and Aldeen
, M.
, 1995
, “Robust Stability of Singularly Perturbed Discrete-Delay Systems
,” IEEE Trans. Autom. Control
, AC-40
, pp. 1620
–1623
.3.
Stepan, G., 1989, Retarded Dynamical Systems, Longman, London.
4.
Stepan, G., Enikov, E., and Muller, T., 1996–1997, “Nonlinear Dynamics of Computer Controlled Machines,” Proceedings of 11th CISM-IFTOMM Symposium on Theory and Practice of Robots and Manipulators, Udine, 1996, Morecki, A., Bianchi, G. eds., Springer, Berlin, 1997, pp. 81–88.
5.
Olgac
, N.
, and Elmali
, H.
, 2000
, “Analysis and Design of Delayed Resonator in Discrete Domain
,” J. Vib. Control
, 6
, pp. 273
–289
.6.
Kokotovic, P. V., Khalil, H. K., and O’Reilly, J., 1986, Singular Perturbation Methods in Control: Analysis and Design, Academic Press, New York.
7.
Khalil
, H. K.
, 1989
, “Feedback Control of Nonstandard Singularly Perturbed Systems
,” IEEE Trans. Autom. Control
, AC-34
, pp. 1052
–1060
.8.
Hsiao
, F. H.
, and Hwang
, J. D.
, 1996
, “Stabilization of Nonlinear Singularly Perturbed Multiple Time-Delay Systems by Dither
,” ASME J. Dyn. Syst., Meas., Control
, 18
, pp. 176
–181
.9.
Shi
, P.
, Shue
, S. P.
, and Agarwal
, R. K.
, 1998
, “Robust Disturbance Attenuation with Stability for a Class of Uncertain Singularly Perturbed Systems
,” Int. J. Control
, 70
, pp. 873
–891
.10.
Li
, T. H. S.
, and Li
, J. H.
, 1992
, “Stabilization Bound of Discrete Two-Time-Scale Systems
,” Syst. Control Lett.
, 18
, pp. 479
–489
.11.
Hsiao
, F. H.
, Pan
, S. T.
, and Teng
, C. C.
, 1999
, “An Efficient Algorithm for Finding the D-Stability Bound of Discrete Singularly Perturbed Systems with Multiple Time Delays
,” Int. J. Control
, 72
, pp. 1
–17
.12.
Phoojaruenchanachai
, S.
, Uahchinkul
, K.
, and Prempraneerach
, Y.
, 1998
, “Robust Stabilization of a State Delayed System
,” IEE Proc.-D:Control Theory Appl.
145
, pp. 87
–91
.13.
Lien
, C. H.
, Hsieh
, J. G.
, and Sun
, Y. J.
, 1998
, “Robust Stabilization for a Class of Uncertain Systems with Multiple Time Delays via Linear Control
,” J. Math. Anal. Appl.
, 218
, pp. 369
–378
.14.
Wu
, H. S.
, and Mizukami
, K.
, 1994
, “Robust Stabilization of Uncertain Linear Dynamical Systems with Time-Varying Delay
,” J. Optim. Theory Appl.
, 82
, pp. 593
–606
.15.
Naidu, D. S., and Rao, A. K., 1985, Singular Perturbation Analysis of Discrete Control Systems, Springer-Verlag, Berlin.
16.
Hsiao
, F. H.
, Pan
, S. T.
, and Teng
, C. C.
, 1997
, “D-Stability Bound Analysis for Discrete Multiparameter Singularly Perturbed Systems
,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl.
, 44
, pp. 347
–351
.17.
Mahmoud
, M. S.
, 1982
, “Order Reduction and Control of Discrete Systems
,” IEE Proc.-D: Control Theory Appl.
129
, pp. 129
–135
.18.
Hsia, T. C., 1977, System Identification, Lexington, New York.
19.
Vidyasagar, M., 1985, Control System Synthesis, MIT Press, Cambridge.
Copyright © 2002
by ASME
You do not currently have access to this content.
