Full Text:   <3573>

CLC number: TP273

On-line Access: 

Received: 2007-09-22

Revision Accepted: 2008-01-28

Crosschecked: 0000-00-00

Cited: 8

Clicked: 6046

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

Journal of Zhejiang University SCIENCE A 2008 Vol.9 No.8 P.1034-1042

http://doi.org/10.1631/jzus.A0720008


Delay-dependent robust control for uncertain discrete singular systems with time-varying delay


Author(s):  Hui-jiao WANG, Xiao-dong ZHAO, An-ke XUE, Ren-quan LU

Affiliation(s):  Institute of Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China; more

Corresponding email(s):   hjwang@hdu.edu.cn

Key Words:  Uncertain discrete singular system, Time-varying delay, Robust control, Linear matrix inequality (LMI)


Hui-jiao WANG, Xiao-dong ZHAO, An-ke XUE, Ren-quan LU. Delay-dependent robust control for uncertain discrete singular systems with time-varying delay[J]. Journal of Zhejiang University Science A, 2008, 9(8): 1034-1042.

@article{title="Delay-dependent robust control for uncertain discrete singular systems with time-varying delay",
author="Hui-jiao WANG, Xiao-dong ZHAO, An-ke XUE, Ren-quan LU",
journal="Journal of Zhejiang University Science A",
volume="9",
number="8",
pages="1034-1042",
year="2008",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A0720008"
}

%0 Journal Article
%T Delay-dependent robust control for uncertain discrete singular systems with time-varying delay
%A Hui-jiao WANG
%A Xiao-dong ZHAO
%A An-ke XUE
%A Ren-quan LU
%J Journal of Zhejiang University SCIENCE A
%V 9
%N 8
%P 1034-1042
%@ 1673-565X
%D 2008
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A0720008

TY - JOUR
T1 - Delay-dependent robust control for uncertain discrete singular systems with time-varying delay
A1 - Hui-jiao WANG
A1 - Xiao-dong ZHAO
A1 - An-ke XUE
A1 - Ren-quan LU
J0 - Journal of Zhejiang University Science A
VL - 9
IS - 8
SP - 1034
EP - 1042
%@ 1673-565X
Y1 - 2008
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A0720008


Abstract: 
The design problem of delay-dependent robust control for uncertain discrete singular systems with time-varying delay is addressed in this paper. The uncertainty is assumed to be norm-bounded. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent robust stability condition is derived and expressed in terms of linear matrix inequalities (LMIs). A suitable robust state feedback control law is presented, which guarantees that the resultant closed-loop system is regular, causal and stable for all admissible uncertainties. Numerical examples are given to demonstrate the applicability of the proposed method.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Boukas, E.K., Liu, Z.K., 2003. Delay-dependent stability analysis of singular linear continuous-time systems. IEE Proc.-Control Theory Appl., 150(4):325-330.

[2] Chen, S.H., Chou, J.H., 2003. Stability robustness of linear discrete singular time-delay systems with structured parameter uncertainties. IEE Proc.-Control Theory Appl., 150(3):295-302.

[3] Chen, S.J., Lin, J.L., 2004. Robust stability of discrete time-delay uncertain singular systems. IEE Proc.-Control Theory Appl., 151(1):45-52.

[4] Chen, Y., Xue, A., Ge, M., Wang, J., Lu, R., 2007. On exponential stability for systems with state delays. J. Zhejiang Univ. Sci. A, 8(8):1296-1303.

[5] Dai, L., 1989. Singular Control Systems. Springer-Verlag, Berlin, Germany.

[6] Fridman, E., 2001. A Lyapunov Based Approach to Stability of Descriptor Systems with Delays. IEEE Proc. 40th Conf. on Decision and Control, p.2850-2855.

[7] Fridman, E., Shaked, U., 2002. A descriptor approach to H control of linear time-delay systems. IEEE Trans. on Automatic Control, 47(2):253-270.

[8] Gao, H., Chen, T., 2007. New results on stability of discrete-time systems with time-varying state delay. IEEE Trans. on Automatic Control, 52(2):328-334.

[9] Gao, H., Lam, J., Wang, C., Wang, Y., 2004. Delay-dependent output-feedback stabilization of discrete-time systems with time-varying state delay. IEE Proc.-Control Theory Appl., 151(6):691-698.

[10] Gu, K., Kharitonov, V.L., Chen, J., 2003. Stability of Time-delay Systems. Birkhauser, Boston.

[11] Han, Q.L., 2002a. Robust stability of uncertain delay-differential systems of neutral type. Automatica, 38(4):719-723.

[12] Han, Q.L., 2002b. New results for delay-dependent stability of linear systems with time-varying delay. Int. J. Syst. Sci., 33(3):213-228.

[13] Han, Q.L., 2004a. On robust stability of neutral systems with time-varying discrete delay and norm-bounded uncertainty. Automatica, 40(6):1087-1092.

[14] Han, Q.L., 2004b. A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays. Automatica, 40(10):1791-1796.

[15] Han, Q.L., 2005a. Stability analysis for a partial element equivalent circuit (PEEC) model of neutral type. Int. J. Circuit Theory Appl., 33(4):321-332.

[16] Han, Q.L., 2005b. On stability of linear neutral systems with mixed time-delays: a discretized Lyapunov functional approach. Automatica, 41(7):1209-1218.

[17] Han, Q.L., 2005c. Absolute stability of time-delay systems with sector-bounded nonlinearity. Automatica, 41(12):2171-2176.

[18] Han, Q.L., Yu, X., Gu, K., 2004. On computing the maximum time-delay bound for stability of linear neutral systems. IEEE Trans. on Automatic Control, 49(12):2281-2286.

[19] Ji, X., Su, H., Chu, J., 2006. Delay-dependent Robust Stability of Uncertain Discrete Singular Time-delay Systems. Proc. American Control Conf., p.3843-3848.

[20] Jiang, X., Han, Q.L., 2005. On H control for linear systems with interval time-varying delay. Automatica, 41(12):2099-2106.

[21] Jiang, X., Han, Q.L., 2006. Delay-dependent robust stability for uncertain linear systems with interval time-varying delay. Automatica, 42:1059-1065.

[22] Lewis, F.L., 1986. A survey of linear singular systems. Circuits Syst. Signal Process., 5(1):3-36.

[23] Petersen, I.R., 1987. A stabilization algorithm for a class of uncertain linear systems. Syst. Control Lett., 8(4):351-357.

[24] Wang, H., Xue, A., Lu, R., Xu, Z., Wang, J., 2007. Robust H control for discrete singular systems with parameter uncertainties. Acta Automatica Sinica, 33:1300-1305 (in Chinese).

[25] Wang, H., Xue, A., Guo, Y., Lu, R., 2008. Input-output approach to robust stability and stabilization for uncertain singular systems with time-varying discrete and distributed delays. J. Zhejiang Univ. Sci. A, 9(4):546-551.

[26] Wang, R., Liu, Y., 2000. Asymptotic Stability and Robustness for Discrete-time Singular Systems with Multiple Delays. Proc. World Congress in Intelligent Control and Automation, p.3350-3353.

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

[28] Xu, S., Dooren, P.V., Stefan, R., Lam, J., 2002. Robust stability and stabilization for singular systems with state delay and parameter uncertainty. IEEE Trans. on Automatic Control, 47(7):1122-1128.

[29] Yue, D., Han, Q.L., 2005a. Delay-dependent robust H controller design for uncertain descriptor systems with time-varying discrete and distributed delays. IEE Proc. Control Theory Appl., 152(6):628-638.

[30] Yue, D., Han, Q.L., 2005b. Delayed feedback control of uncertain systems with time-varying input delay. Automatica, 41(2):233-240.

[31] Zhang, X.M., Han, Q.L., 2006. Delay-dependent robust H filtering for uncertain discrete-time systems with time-varying delay based on a finite sum inequality. IEEE Trans. on Circuits Syst.-II: Expr. Briefs, 53(12):1466-1470.

[32] Zhou, S., Lam, L., 2003. Robust stabilization of delayed singular systems with linear fractional parametric uncertainties. Circuits Syst. Signal Process., 22(6):579-588.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE