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Boukas, El-Kébir

Delay-dependent robust stabilizability of singular linear systems with delays. (English) Zbl 1167.93396

Stochastic Anal. Appl. 27, No. 4, 637-655 (2009).
Summary: This article deals with the class of continuous-time singular uncertain linear systems with time-varying delay in the state vector. The uncertainties we are considering are of norm bounded type. Delay-dependent sufficient conditions on robust stability and robust stabilizability are developed. A design algorithm for a memoryless state feedback controller which guarantees that the closed-loop dynamics will be regular, impulse-free, and robust stable is proposed in terms of the solutions to linear matrix inequalities.

Cited in 5 Documents

MSC:

93D21 Adaptive or robust stabilization
93D09 Robust stability
93D15 Stabilization of systems by feedback
15A39 Linear inequalities of matrices
93C15 Control/observation systems governed by ordinary differential equations
93C41 Control/observation systems with incomplete information

Keywords:

continuous-time uncertain linear systems; linear matrix inequality; memoryless state feedback; norm bounded type uncertainties; robust stability; robust stabilizability; singular systems
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\textit{E.-K. Boukas}, Stochastic Anal. Appl. 27, No. 4, 637--655 (2009; Zbl 1167.93396)
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References:

[1] DOI: 10.1007/BFb0002475
[2] DOI: 10.1007/BF01600184 · Zbl 0613.93029
[3] Chun-Hsiung F., Proceedings of the American Control Conference pp 1971– (1998)
[4] DOI: 10.1002/1521-4001(200104)81:4<219::AID-ZAMM219>3.0.CO;2-H
[5] DOI: 10.1049/ip-cta:19981861
[6] DOI: 10.1016/0167-6911(94)00041-S · Zbl 0883.93035
[7] DOI: 10.1109/TAC.1981.1102763 · Zbl 0541.34040
[8] DOI: 10.1109/81.995677 · Zbl 1368.93513
[9] Fridman E., Proceedings of the 40th IEEE Conference on Control and Decision pp 2850– (2001)
[10] DOI: 10.1109/9.983353 · Zbl 1364.93209
[11] Kim J.H., American Control Conference 1 pp 620– (2002)
[12] DOI: 10.1109/TAC.2003.814276 · Zbl 1364.93644
[13] DOI: 10.1109/TAC.2002.800651 · Zbl 1364.93723
[14] DOI: 10.1109/TAC.2003.822854 · Zbl 1365.93375
[15] DOI: 10.1016/S0005-1098(99)00061-8 · Zbl 0959.93048
[16] Rehm A., IFAC World Congress. (2002)
[17] DOI: 10.1007/s10957-005-6538-5 · Zbl 1101.93077
[18] DOI: 10.1007/978-1-4612-0077-2
[19] DOI: 10.1109/TAC.2004.831109 · Zbl 1365.93226
[20] Han Q.L., Automatica 40 pp 1971– (2004)
[21] DOI: 10.1109/TAC.2002.806665 · Zbl 1364.34102
[22] DOI: 10.1016/j.automatica.2003.07.004 · Zbl 1046.93015
[23] DOI: 10.1109/TAC.2003.811269 · Zbl 1364.93591
[24] DOI: 10.1016/S0005-1098(03)00167-5 · Zbl 1145.93302
[25] DOI: 10.1016/j.automatica.2004.03.004 · Zbl 1059.93108
[26] DOI: 10.1016/j.automatica.2003.10.005 · Zbl 1034.93058
[27] DOI: 10.1109/9.975503 · Zbl 1006.93055
[28] June , F. , Shuqian , Z. , and Zhaolin , C. 2002 . Guaranteed cost control of linear uncertain singular time-delay systems . Proceedings of the 41th, IEEE Conference on Decision and Control , Las Vegas , Nevada , pp. 1802 – 1807 .
[29] DOI: 10.1002/aic.690410319
[30] DOI: 10.1016/S0005-1098(96)00193-8 · Zbl 0881.93024
[31] DOI: 10.1109/TCS.1981.1084908
[32] DOI: 10.1111/j.1934-6093.2003.tb00132.x
[33] Debeljkovic D.Lj., International Journal of Information & System Science 2 (1) pp 1– (2006)
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.