Robust D -stability analysis for linear discrete-time singular systems with structured parameter uncertainties and delayed perturbations

Abstract

In this paper, the robust D-stability problem (i.e. robust eigenvalue-clustering in a specified circular region problem) of linear discrete-time singular systems with structured (elemental) parameter uncertainties and delayed perturbations is investigated. Under the assumptions that the nominal discrete-time singular system is regular and impulse free and has all its finite eigenvalues lying inside a specified circular region, a new sufficient condition is proposed to preserve the assumed properties when the structured (elemental) parameter uncertainties and delayed perturbations are added into the nominal discrete-time singular system. When all the finite eigenvalues lie inside the unit circle of the z plane, the proposed criterion will become the stability robustness criterion. An example is given to demonstrate the applicability of the proposed sufficient condition.

Keywords

singular systems structured parameter uncertainties delayed perturbations

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References

Fang

C. H.

Lee

Chang

F. R.

Robust control analysis and design for discrete-time singular systems. Automatica, 1994, 30, 1741–1750.

Fang

C. H.

Robust stability of generalized state-space systems. PhD dissertation, Department of Electrical Engineering, National Sun Yat-Sen University, Taiwan, 1997.

Chou

J. H.

Liao

W. H.

Regional eigenvalue-clustering robustness analysis for singular systems with structured parameter perturbations. Proc. Instn Mech. Engrs, Part I: J. Systems and Control Engineering, 1998, 212 (16), 467–471.

Chou

J. H.

Chen

S. H.

Hsieh

C. H.

Regional eigenvalue-clustering robustness analysis of singular systems with structured and unstructured parameter uncertainties. In Proceedings of the 2000 Automatic Control Conference, Taiwan, 2000, pp. 18–23.

Lewis

F. L.

A survey of linear singular systems. Circuit, Systems Signal Processing, 1986, 5, 3–36.

Liu

Y. Q.

Xie

X. S.

Stability, Stabilization and Control for Singular Large Scale Systems with Delay, 1998 (South China University of Technology Press, Canton).

Dai

Singular Control Systems, 1989 (Springer-Verlag, Berlin).

Chen

K. H.

Robust analysis and design of multiloop control systems. PhD dissertation, National Tsing-Hua University, Taiwan, 1989.

Ortega

J. M.

Numerical Analysis, 1972 (Academic Press, New York).

10.

Chen

C. T.

Linear Systems Theory and Design, 1984 (Holt, Rinehart and Winston, New York).