Stabilization of Discrete Singularly Perturbed Systems Under Composite Observer-Based Control

[+] Author and Article Information
Feng-Hsiag Hsiao

Department of Electrical Engineering, Chang Gung University, 259, Wen-Hwa 1st Road, Kwei-San, Taoyuan Shian, Taiwan 333, R.O.C.

Jiing-Dong Hwang

Department of Electronic Engineering, Jin-Wen Institute of Technology, 99, An Chung Road, Hsin Tien, Taipei, Taiwan 231, R.O.C.

Shing-Tai Pan

Department of Electrical Engineering, Kao Yuan Institute of Technology, 1821, Chung-Shan Road, Lu-Ghu Hsiang, Kaohsiung, Taiwan 821, R.O.C.

J. Dyn. Sys., Meas., Control 123(1), 132-139 (Feb 02, 1999) (8 pages) doi:10.1115/1.1285759 History: Received February 02, 1999
Copyright © 2001 by ASME
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Kokotovic, P. V., Khalil, H. K., and O’Reilly, J., 1986, Singular Perturbation Methods in Control: Analysis and Design, Academic Press, New York.
Li,  T. H. S., and Li,  J. H., 1992, “Stabilization Bound of Discrete Two-Time-Scale Systems,” Syst. Control Lett., 18, pp. 479–489.
Litkouhi,  B., and Khalil,  H., 1985, “Multirate and Composite Control of Two-Time-Scale Discrete-Time Systems,” IEEE Trans. Autom. Control., 30, pp. 645–651.
Feng,  W., 1988, “Characterization and Computation for The Bound ε* in Linear Time-invariant Singularly Perturbed Systems,” Syst. Control Lett., 11, pp. 195–202.
Chen,  B. S., and Lin,  C. L., 1990, “On The Stability Bounds of Singularly Perturbed Systems,” IEEE Trans. Autom. Control., 35, pp. 1265–1270.
Sen,  S., and Datta,  K. B., 1993, “Stability Bounds of Singularly Perturbed Systems,” IEEE Trans. Autom. Control., 38, pp. 302–304.
Pan,  S. T., Hsiao,  F. H., and Teng,  C. C., 1996, “Stability Bound of Multiple Time-delay Singularly Perturbed Systems,” Electron. Lett., 32, pp. 1327–1328.
Hsiao,  F. H., Pan,  S. T., and Teng,  C. C., 1997, “D-Stabilization Bound Analysis for Discrete Multiparameter Singularly Perturbed Systems,” IEEE Trans. Circuits Syst., Part I, 44, pp. 347–351.
Naidu, D. S., and Rao, A. K., 1985, Singular Perturbation Analysis of Discrete Control Systems, Springer-Verlag, Berlin.
Chou,  J. H., and Chen,  B. S., 1990, “New Approach for The Stability Analysis of Interval Matrices,” Control-Theory and Advanced Technology, 6, pp. 725–730.
Mahmoud,  M. S., 1982, “Order Reduction and Control of Discrete Systems,” IEE Proceeding—Control Theory Appl., 129, pp. 129–135.
Saksena,  V. R., O’Reilly,  J., and Kokotovic,  P. V., 1984, “Singular Perturbations and Time Scale Methods in Control Theory—Survey 1976–1983,” Automatica, 20, pp. 273–293.
Oloomi,  H., and Sawan,  M. E., 1987, “The Observer-Based Controller Design of Discrete-Time Singularly Perturbed Systems,” IEEE Trans. Autom. Control., 32, pp. 246–248.
Li,  J. H., and Li,  T. H. S., 1995, “On the Composite and Reduced Observer-based Control of Discrete Two-Time-Scale Systems,” J. Franklin Inst., 332b, pp. 47–66.
Wang,  M. S., Li,  T. H. S., and Sun,  Y. Y., 1996, “Design of Near-Optimal Observer-Based Controllers for Singularly Perturbed Discrete Systems,” JSME International Journal: Series C, 39, pp. 234–241.
John, W. D., 1967, Applied Complex Variables, Macmillan, New York.


Grahic Jump Location
The observer-based controller for the slow subsystem (Eqs. (3.1))
Grahic Jump Location
The observer-based controller for the fast subsystem (Eqs. (3.5))
Grahic Jump Location
The functions ρ[Δ̃1(ε,e )] and ρ[Δ̃2(ε,e )] in (4.6) with ε+0.02
Grahic Jump Location
The suprema of ρ[Δ̃1(ε,e )] and ρ[Δ̃2(ε,e )] in the range θ∊[0,2π)



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