×
Wu, Min; He, Yong; She, Jin-Hua; Liu, Guo-Ping

Delay-dependent criteria for robust stability of time-varying delay systems. (English) Zbl 1059.93108

Automatica 40, No. 8, 1435-1439 (2004).
Summary: This paper deals with the problem of delay-dependent robust stability for systems with time-varying structured uncertainties and time-varying delays. Some new delay-dependent stability criteria are devised by taking the relationship between the terms in the Leibniz-Newton formula into account. Since free weighting matrices are used to express this relationship and since appropriate ones are selected by means of linear matrix inequalities, the new criteria are less conservative than existing ones. Numerical examples suggest that the proposed criteria are effective and are an improvement over previous ones.

Cited in 270 Documents

MSC:

93D09 Robust stability
93C23 Control/observation systems governed by functional-differential equations

Keywords:

Delay-dependent criteria; Robust stability; Time-varying delay; Time-varying structured uncertainties; Linear matrix inequality
PDF BibTeX XML Cite
\textit{M. Wu} et al., Automatica 40, No. 8, 1435--1439 (2004; Zbl 1059.93108)
Full Text: DOI

References:

[1] Boyd, S.; EL Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear matrix inequality in system and control theory. Studies in Applied Mathematics (1994), SIAM: SIAM Philadelphia · Zbl 0816.93004
[2] Cao, Y. Y.; Sun, Y. X.; Cheng, C. W., Delay-dependent robust stabilization of uncertain systems with multiple state delays, IEEE Transactions on Automatic Control, 43, 1608-1612 (1998) · Zbl 0973.93043
[3] de Souza, C. E.; Li, X., Delay-dependent robust \(H_∞\) control of uncertain linear state-delayed systems, Automatica, 35, 1313-1321 (1999) · Zbl 1041.93515
[4] Fridman, E., New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems, Systems and Control Letters, 43, 309-319 (2001) · Zbl 0974.93028
[5] Fridman, E.; Shaked, U., An improved stabilization method for linear time-delay systems, IEEE Transactions on Automatic Control, 47, 1931-1937 (2002) · Zbl 1364.93564
[6] Fridman, E.; Shaked, U., Delay-dependent stability and \(H_∞\) controlConstant and time-varying delays, International Journal of Control, 76, 48-60 (2003) · Zbl 1023.93032
[7] Gu, K.; Kharitonov, V. L.; Chen, J., Stability of time-delay systems (Control Engineering) (2003), Springer: Springer Berlin · Zbl 1039.34067
[8] Gu, K.; Niculescu, S. I., Additional dynamics in transformed time delay systems, IEEE Transactions on Automatic Control, 45, 572-575 (2000) · Zbl 0986.34066
[9] Gu, K.; Niculescu, S. I., Further remarks on additional dynamics in various model transformations of linear delay systems, IEEE Transactions on Automatic Control, 46, 497-500 (2001) · Zbl 1056.93511
[10] Gu, Y.; Wang, S.; Li, Q.; Cheng, Z.; Qian, J., On delay-dependent stability and decay estimate for uncertain systems with time-varying delay, Automatica, 34, 1035-1039 (1998) · Zbl 0951.93059
[11] Hale, J. K.; Verduyn Lunel, S. M., Introduction to functional differential equations (1993), Springer: Springer New York · Zbl 0787.34002
[12] Han, Q. L., New results for delay-dependent stability of linear systems with time-varying delay, International Journal of Systems Science, 33, 213-228 (2002) · Zbl 1031.93138
[13] Han, Q. L., Robust stability of uncertain delay-differential systems of neutral type, Automatica, 38, 719-723 (2002) · Zbl 1020.93016
[14] Han, Q. L.; Gu, K. Q., On robust stability of time-delay systems with norm-bounded uncertainty, IEEE Transactions on Automatic Control, 46, 1426-1431 (2001) · Zbl 1006.93054
[15] Kim, J. H., Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty, IEEE Transactions on Automatic Control, 46, 789-792 (2001) · Zbl 1008.93056
[16] Li, X.; de Souza, C. E., Delay-dependent robust stability and stabilization of uncertain linear delay systemsA linear matrix inequality approach, IEEE Transactions on Automatic Control, 42, 1144-1148 (1997) · Zbl 0889.93050
[17] Moon, Y. S.; Park, P.; Kwon, W. H.; Lee, Y. S., Delay-dependent robust stabilization of uncertain state-delayed systems, International Journal of Control, 74, 1447-1455 (2001) · Zbl 1023.93055
[18] Park, P., A delay-dependent stability criterion for systems with uncertain time-invariant delays, IEEE Transactions on Automatic Control, 44, 876-877 (1999) · Zbl 0957.34069
[19] Su, T. J.; Huang, C. G., Robust stability of delay dependence for linear uncertain systems, IEEE Transactions on Automatic Control, 37, 1656-1659 (1992) · Zbl 0770.93077
[20] Xie, L., Output feedback \(H_∞\) control of systems with parameter uncertainty, International Journal of Control, 63, 741-750 (1996) · Zbl 0841.93014
[21] Yue, D.; Won, S., An improvement on ‘Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty’, IEEE Transactions on Automatic Control, 47, 407-408 (2002) · Zbl 1364.93609
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.