×

zbMATH — the first resource for mathematics

Less conservative delay-dependent stability criteria for linear systems with interval time-varying delays. (English) Zbl 1307.93308
Summary: This article provides new delay-dependent stability criteria for linear systems with interval time-varying delays. With a new Lyapunov-Krasovskii functional constructed, a tighter upper bound of its derivative is estimated. The resulting criterion has an advantage over some existing ones in the literature due to the fact that it involves fewer matrix variables and is less conservative, which is established theoretically. Two numerical examples are given to demonstrate the reduced conservatism of the proposed results.

MSC:
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C15 Control/observation systems governed by ordinary differential equations
93C05 Linear systems in control theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1109/9.983353 · Zbl 1364.93209 · doi:10.1109/9.983353
[2] DOI: 10.1016/j.automatica.2009.08.002 · Zbl 1180.93080 · doi:10.1016/j.automatica.2009.08.002
[3] Gu, K. (2000), ’An Integral Inequality in the Stability Problem of Time-delay Systems’, inProceedings of 39th IEEE Conference on Decision and Control, Sydney, Australia, pp. 2805–2810
[4] DOI: 10.1080/00207170110047190 · Zbl 1015.93053 · doi:10.1080/00207170110047190
[5] Gu, K. and Han, Q.L. (2000), ’Discretized Lyapunov Functional for Linear Uncertain Systems with Time-varying Delay’, inProceedings of American Control Conference, Chicago, IL, USA, pp. 1375–1379
[6] DOI: 10.1080/00207170010031486 · Zbl 1015.34061 · doi:10.1080/00207170010031486
[7] DOI: 10.1007/978-1-4612-0039-0 · doi:10.1007/978-1-4612-0039-0
[8] DOI: 10.1109/9.847747 · Zbl 0986.34066 · doi:10.1109/9.847747
[9] DOI: 10.1080/00207720110092207 · Zbl 1031.93138 · doi:10.1080/00207720110092207
[10] DOI: 10.1016/j.automatica.2005.08.005 · Zbl 1100.93519 · doi:10.1016/j.automatica.2005.08.005
[11] DOI: 10.1016/j.automatica.2005.08.005 · Zbl 1100.93519 · doi:10.1016/j.automatica.2005.08.005
[12] DOI: 10.1016/j.automatica.2008.08.005 · Zbl 1158.93385 · doi:10.1016/j.automatica.2008.08.005
[13] DOI: 10.1111/j.1934-6093.2001.tb00056.x · doi:10.1111/j.1934-6093.2001.tb00056.x
[14] DOI: 10.1016/j.automatica.2006.08.015 · Zbl 1111.93073 · doi:10.1016/j.automatica.2006.08.015
[15] DOI: 10.1016/j.automatica.2005.06.012 · Zbl 1100.93017 · doi:10.1016/j.automatica.2005.06.012
[16] DOI: 10.1016/j.automatica.2008.02.020 · Zbl 1155.93405 · doi:10.1016/j.automatica.2008.02.020
[17] DOI: 10.1016/S0167-6911(00)00003-7 · Zbl 0977.93072 · doi:10.1016/S0167-6911(00)00003-7
[18] DOI: 10.1109/9.920802 · Zbl 1008.93056 · doi:10.1109/9.920802
[19] DOI: 10.1080/00207170110067116 · Zbl 1023.93055 · doi:10.1080/00207170110067116
[20] DOI: 10.1109/9.754838 · Zbl 0957.34069 · doi:10.1109/9.754838
[21] DOI: 10.1016/j.automatica.2007.02.022 · Zbl 1120.93043 · doi:10.1016/j.automatica.2007.02.022
[22] DOI: 10.1016/S0005-1098(03)00167-5 · Zbl 1145.93302 · doi:10.1016/S0005-1098(03)00167-5
[23] DOI: 10.1109/TCSII.2007.916727 · doi:10.1109/TCSII.2007.916727
[24] DOI: 10.1016/j.jmaa.2007.12.063 · Zbl 1141.93025 · doi:10.1016/j.jmaa.2007.12.063
[25] DOI: 10.1016/j.automatica.2008.09.010 · Zbl 1168.93387 · doi:10.1016/j.automatica.2008.09.010
[26] Suplin, V. Fridman, E., and Shaked, U. (2004), ’A Projection Approach toHControl of Time-delay Systems’, inProceedings of IEEE conference on Decision and Control, Atlantis, Bahamas, pp. 4548–4553
[27] DOI: 10.1016/j.automatica.2009.11.002 · Zbl 1205.93139 · doi:10.1016/j.automatica.2009.11.002
[28] DOI: 10.1016/j.sysconle.2006.06.006 · Zbl 1117.93072 · doi:10.1016/j.sysconle.2006.06.006
[29] DOI: 10.1016/j.automatica.2004.03.004 · Zbl 1059.93108 · doi:10.1016/j.automatica.2004.03.004
[30] DOI: 10.1109/TAC.2005.843873 · Zbl 1365.93376 · doi:10.1109/TAC.2005.843873
[31] DOI: 10.1109/TAC.2006.886495 · Zbl 1366.93451 · doi:10.1109/TAC.2006.886495
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.