Robust D stabilization of singular systems with polytopic uncertainties

被引：2

作者：

Bai J. ^{[1
]}

Su H. ^{[1
]}

Ji X. ^{[2
]}

Gao J. ^{[3
]}

机构：

[1] State Key Laboratory of Industrial Control Technology, Institute of Cyber-System and Control, Zhejiang University

[2] School of Electrical and Information Engineering, Jiangsu University

[3] Institute of Automation, Zhejiang Sci-Tech University

来源：

Journal of Control Theory and Applications | 2010年 / 8卷 / 4期

基金：

中国国家自然科学基金;

关键词：

Free matrices; LMI region; Robust D stabilization; Singular system;

D O I：

10.1007/s11768-010-8077-3

中图分类号：

学科分类号：

摘要：

The robust D stabilization problem is considered for singular systems with polytopic uncertainties in this paper. Both the derivative matrix E and the state matrix A are with uncertainties, which were not considered before. First, with the introduction of some free matrices, a necessary and sufficient condition for the singular system to be D stable is proposed, based on which, the robust D stable problem is solved, and a sufficient condition for the closed system to be robust D stabilizable is obtained. The desired state feedback controller is given in an explicit expression. Numerical examples show the efficiency of the proposed approach. © 2010 South China University of Technology, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg.

引用

页码：540 / 544

页数：4

共 13 条

[1]

Hsiung K.L., Lee L., Lyapunov inequality and bounded real lemma for discrete-time descriptor systems[J], IEE Proceedings on Control Theory and Applications, 146, 4, pp. 327-331, (1999)

[2]

Dai L., Singular Control Systems[M], (1989)

[3]

Masubuchi I., Kamitane Y., Ohara A., Et al., H<sub>∞</sub> control for descriptor systems: A matrix inequalities approach[J], Automatic, 33, 4, pp. 669-673, (1997)

[4]

Lin C., Wang Q., Lee T.H., Robust normalization and stabilization of uncertain descriptor systems with norm-bounded perturbations[J], IEEE Transactions on Automatic Control, 50, 4, pp. 515-520, (2005)

[5]

Chu D., Ho D.W.C., Necessary and sufficient conditions for the output feedback regularization of descriptor systems[J], IEEE Transactions on Automatic Control, 44, 2, pp. 405-412, (1999)

[6]

Varga A., On stabilization methods of descriptor systems[J], System & Control Letters, 24, 2, pp. 133-138, (1995)

[7]

Xu S., Lam J., Robust stability and stabilization for singular systems with state delay and parameter uncertainty[J], IEEE Transactions on Automatic Control, 47, 7, pp. 1122-1128, (2002)

[8]

Xu S., Lam J., Robust stability and stabilization of discrete singular systems: An equivalent characterization[J], IEEE Transactions on Automatic Control, 49, 4, pp. 568-574, (2004)

[9]

Su H., Ji X., Chu J., Delay-dependent robust control for uncertain singular time-delay systems[J], Asian Journal of Control, 8, 2, pp. 180-189, (2006)

[10]

Chilali M., Gahinet P., H<sub>∞</sub> design with pole placement constraints: An LMI approach[J], IEEE Transactions on Automatic Control, 41, 3, pp. 358-367, (1996)

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