» Download Article

Authors
Li, Lin; Jia, Yingmin; Du, Junping; Yu, Fashan

Identifier
10.3182/20080706-5-KR-1001.00660

Index Terms
Descriptor systems

Abstract
This paper is devoted to the problem of H-inf output feedback control for linear singular systems with state time-varying delay. The purpose is to design a non-singular dynamic output feedback controller to ensure that the closed-loop system is regular, impulse free and stable with a prescribed H-inf performance level. Using the linear matrix inequality (LMI) approach, a new delay-dependent stability criterion is obtained by introducing a free-weighting matrix when estimating the upper bound of the derivative of Lyapunov Functional. And the corresponding stability controller design algorithm is proposed. Finally, a numerical example is included to demonstrate the effectiveness of the proposed method.

References

REFERENCES
L. Dugard and E. I. Verriest, Stability and Control of Time-
Delay Systems [M]. Berlin: Springer-Verlag, 1998.

Xu Shengyuan, Van Dooren Paul, Stefan Radu and Lam James.
Robust Stability and Stabilization for Singular SystemsWith
State Delay and Parameter Uncertainty. IEEE Transactions
on Automatic Control. volumn 47, pages 1122�C1128, July
2002.

E. Fridman, U. Shaked and L. Xie. Robust H�� filtering of
linear systems with time-varying delay. IEEE Transaction
on Automatic Control, volumn 48, pages 159�C165, 2003.

Y. S. Lee, Y. S. Moon, W. H. Kwon and P. G. Park. Delaydependent
robust H�� control for uncertain state-delayed systems.
Automatica, volumn 40, pages 65�C72, 2004.

Jong Hae Kim. New design method on memoryless H�� control
for singular systems with delayed state and control using
LMI. Journal of the Franklin Institute. pages 321�C327, 2005.
Jia Yingmin. Robust H�� Control. Science Press, pages 144-
214, 2007.

M. S. Mahmout and A. Ismail. New results on delay-dependent
control of time-delay systems. IEEE Transactions on Automatic
Control, volumn 50, pages 95�C100, 2005.

Peng Shi, El-Kbir Boukas. and Ramesh K. Aganval. Robust H��
control of singular continuous-time systems with delays and
uncertainties. Proceedings of the 39th IEEE Conference on
Decision and Control Sidney, volumn 2, pages 1515�C1520,
December 2000.

C. E. De Souza and L. Xie. Delay-dependent robust control
of uncertain linear state-delayed sys- tems. Automatica,
volumn 35, pages 1313�C1321, 1999.

J. L. Lin and S. J. Chen. Robustness Analysis of Uncertain
Linear Singular Systems with Output Feedback Control.
IEEE Transactions on Automatic Control, volumn 40, pages
1924�C1929, 1999.

Jun��e Feng, Weihai Zhang, Zhaolin Cheng and Peng Cui. H��
output feedback control for descriptor systems with delayedstate.
American Control Conference, volumn 7, pages 4892�C
4896, June, 2007.

Zhu Shuqian, Li Zhenbo, Cheng Zhaolin and Feng Jun��e.
Delay-dependent robust stability for uncertain singular timedelay
systems: Dynamic output feedback case. Proceeding
of the 44th IEEE conference on Decision and Control, pages
5065�C5070, Spain, December 2005.

Vladimir L. Kharitonov, Silviu-Iulian Niculescu, Jaime
Moreno, and Wim Michiels. Static Output Feedback Stabilization:
Necessary Conditions for Multiple Delay Controllers.
IEEE Transactions on Automatic Control, volumn
50, pages 82-86, 2006.

V. Suplin, E. Fridman and U. Shaked. H�� control of linear
uncertain time-delay dystems: A projection approach. IEEE
Transactions on Automatic Control, volumn 51, pages 680�C
685, 2006.