A two-time-scale linear system with uncertain time-varying parameter is to be stabilized. A class of robust composite controls is proposed. The control renders the system practically stable regardless of the true value of the parameter. The control scheme consists of linear and nonlinear parts. The linear part is designed via a two-level optimization setting. No matching condition is needed for the linear control. The nonlinear part is of continuous saturation type. Matching condition is needed for the nonlinear control. However, it can be achieved by choosing the boundary layer model appropriately.
Issue Section:
Technical Papers
1.
Barmish
B. R.
1983
, “Stabilization of Uncertain Systems Via Linear Control
,” IEEE Trans. Automatic Control
, Vol. 28
, pp. 848
–850
.2.
Barmish
B. R.
1985
, “Necessary and Sufficient Conditions for Quadratic Stabilizability of an Uncertain System
,” J. Optimization Theory and Applications
, Vol. 46
, pp. 399
–408
.3.
Barmish
B. R.
Leitmann
G.
1982
, “On Ultimate Boundedness Control of Uncertain Systems in the Absence of Matching Conditions
,” IEEE Trans. Automatic Control
, Vol. 27
, pp. 153
–157
.4.
Chen
Y. H.
1986
, “On the Deterministic Performance of Uncertain Dynamical Systems
,” International J. Control
, Vol. 43
, pp. 1557
–1579
.5.
Chen
Y. H.
1987
a, “Robust Output Feedback Controller: Indirect Design
,” International J. Control
, Vol. 46
, pp. 1093
–1103
.6.
Chen
Y. H.
1987
b, “On the Robustness of Mismatched Uncertain Dynamical Systems
,” ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol. 109
, pp. 29
–35
.7.
Chen, Y. H., 1995, “A New Matching Condition for Robust Control Design,” Proc. American Control Conference, San Francisco, CA, pp. 122–126; ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL (published in this issue, pp. 453–458).
8.
Chen, Y. H., and Chen, J. S., 1990, “Robust Control of Uncertain Systems with Time-Varying Uncertainty: A Computer Aided Setup with Illustrations,” Proc. American Control Conference, San Diego, CA, pp. 2643–2648.
9.
Chen
Y. H.
Leitmann
G.
1987
, “Robustness of Uncertain Systems in the Absence of Matching Assumptions
,” International J. Control
, Vol. 45
, pp. 1527
–1542
.10.
Corless
M.
1993
, “Control of Uncertain Nonlinear Systems
,” ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol. 115
, pp. 362
–372
.11.
Corless
M.
Garofalo
F.
Glielmo
L.
1993
, “New Results on Composite Control of Singularly Perturbed Linear Systems
,” Automatica
, Vol. 29
, pp. 387
–340
.12.
Corless
M.
Leitmann
G.
1981
, “Continuous State Feedback Guaranteeing Uniform Ultimate Boundedness for Uncertain Dynamic Systems
,” IEEE Trans. Automatic Control
, Vol. 26
, pp. 1139
–1143
.13.
Corless, M., and Leitmann, G., 1988, “Deterministic Control of Uncertain Systems: A Lyapunov Theory Approach,” Deterministic Control of Uncertain Systems, A. Zinober, ed., IEE Control Engineering Series 40, Peter Peregrinus Ltd., London.
14.
Garofalo, F., and Leitmann, G., 1990, “Nonlinear Composite Control of a Class of Nominally Linear Singularly Perturbed Uncertain Systems,” Deterministic Control of Uncertain Systems, A. Zinober, ed., IEE Control Engineering Series 40, Peter Peregrinus Ltd., London.
15.
Gu, K., and Chen, Y. H., 1989, “Uncertain Systems: New Uncertainty Characterization for Linear Control Design,” Proc. 28th IEEE Conference on Decision and Control, Tampa, FL, pp. 1508–1512.
16.
Gu
K.
Chen
Y. H.
Zohdy
M. A.
Loh
N. K.
1991
, “Quadratic Stabilizability by Linear Control: A Two Level Optimization Setup
,” Automatica
, Vol. 27
, pp. 161
–165
.17.
Gu, K., and Loh, N. K., 1990, “Maximum Bound of Quadratic Stability for Possibly Fast Time-Varying Polytopic Uncertainties,” Proc. American Control Conference, San Diego, CA, pp. 2632–2636.
18.
Kokotovic, P. V., Khalil, H. K., and O’Reilly, J., 1986, Singular Perturbation Methods in Control: Analysis and Design, Academic Press, London.
19.
Leitmann
G.
1993
, “On One Approach to the Control of Uncertain Systems
,” ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol. 115
, pp. 373
–380
.20.
Petersen
I. R.
Hollot
C. V.
1986
, “A Riccati Equation Approach to the Stabilization of Uncertain Linear Systems
,” Automatica
, Vol. 22
, pp. 397
–411
.21.
Saberi
A.
Khalil
H.
1984
, “Quadratic-Type Lyapunov Functions for Singularly Perturbed System
,” IEEE Trans. Automatic Control
, Vol. 29
, pp. 542
–550
.22.
Schmitendorf
W. E.
1988
a, “Designing Stabilizing Controllers for Uncertain Systems Using the Riccati Equation Approach
,” IEEE Trans. Automatic Control
, Vol. 33
, pp. 376
–379
.23.
Schmitendorf
W. E.
1988
b, “Design of Observer-Based Robust Stabilizing Controllers
,” Automatica
, Vol. 24
, pp. 693
–696
.
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