Regional eigenvalue-clustering robustness analysis for singular systems with structured parameter perturbations

Abstract

In this paper, under assumptions that the nominal linear singular system is regular and impulse-free and has all its finite eigenvalues lying inside certain specified regions, a sufficient condition is proposed to preserve the assumed properties when the structured parameter perturbations are added into the nominal singular system. No restriction is imposed on the shapes of the specified regions. The proposed method is applicable to both the continuous-time case and the discrete-time case. When all the finite eigenvalues are just required to locate in the stable region, the proposed criterion will become the stability robustness criterion. By mathematical analysis, the presented criterion is proved to be less conservative than the existing criterion reported recently.

Keywords

eigenvalue clustering singular systems robustness

Get full access to this article

View all access options for this article.

References

Qiu

Davison

E. J.

The stability robustness of generalized eigenvalues. IEEE Trans. Autom. Control, 1992, 37, 886–891.

Fang

C. H.

Chang

F. R.

Analysis of stability robustness for generalized state-space systems with structured perturbations. Systems Control Lett., 1993, 21, 109–114.

Fang

C. H.

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

Lin

Wang

Soh

C. B.

Robustness of uncertain descriptor systems. Systems Control Lett., 1997, 31, 129–138.

Chou

J. H.

Chen

S. H.

Zheng

L. A.

Stability robustness of discrete-time singular systems with structured parameter perturbations. In Proceedings of the Fourth Military Academy Symposium on

Fundamental Science, Taiwan, 1997, pp. 841–849.

Chou

J. H.

Liao

W. H.

Stability robustness of continuous-time perturbed descriptor systems. In Proceedings of the 14th National Conference of the Chinese Society of Mechanical Engineers, Taiwan, 1997, pp. 97–101 (CSME, Taiwan).

Lewis

F. L.

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

Chou

J. H.

Pole-assignment robustness in a specified disk. Systems Control Lett., 1991, 16, 41–44.

Lee

Fang

C. H.

Regional pole-clustering robustness for uncertain generalized state-space systems. In Proceedings of the 33rd IEEE Conference on

Decision and Control, Lake Buena Vista, Florida, 1994, pp. 587–588 (IEEE, New York).

10.

Dai

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

11.

Verghese

G. C.

Levy

B. C.

Kailath

A Generalized state-space for singular systems. IEEE Trans. Autom. Control, 1981, 26, 811–831.

12.

Bender

D. J.

Laub

A. J.

The linear-quadratic optimal regulator for descriptor systems. IEEE Trans. Autom. Control, 1987, 32, 672–687.

13.

Juang

Y.T.

Kuo

T. S.

Hsu

C. F.

Stability robustness analysis of digital control systems in state-space models. Int. J. Systems Sci., 1987, 46, 1547–1556.

14.

Ortega

J. M.

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

15.

Chen

C. T.

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

16.

Juang

Y. T.

Eigenvalue assignment robustness: The analysis for autonomous system matrices. Int. J. Control, 1989, 49, 1787–1797.