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A survey of linear matrix inequality techniques in stability analysis of delay systems. (English) Zbl 1156.93382

Summary: Recent years have witnessed a resurgence of research interests in analysing the stability of time-delay systems. Many results have been reported using a variety of approaches and techniques. However, much of the focus has been laid on the use of the Lyapunov-Krasovskii theory to derive sufficient stability conditions in the form of linear matrix inequalities. The purpose of this article is to survey the recent results developed to analyse the asymptotic stability of time-delay systems. Both delay-independent and delay-dependent results are reported in the article. Special emphases are given to the issues of conservatism of the results and computational complexity. Connections of certain delay-dependent stability results are also discussed.

MSC:

93D20 Asymptotic stability in control theory
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References:

[1] Boukas E-K, Deterministic and Stochastic Time Delay Systems (2002)
[2] DOI: 10.1049/ip-cta:20020442
[3] Boyd S, in SIAM Studies in Applied Mathematics (1994)
[4] DOI: 10.1109/9.728880 · Zbl 0973.93043
[5] DOI: 10.1049/ip-cta:19981951
[6] DOI: 10.1016/j.fss.2006.01.010 · Zbl 1106.93046
[7] DOI: 10.1109/TFUZZ.2004.840112 · Zbl 05452507
[8] Chen B, International Journal of Innovative Computing, Information and Control 2 pp 293– (2006)
[9] DOI: 10.1109/TFUZZ.2005.856562 · Zbl 05452502
[10] DOI: 10.1109/9.412637 · Zbl 0834.93044
[11] DOI: 10.1049/el:20001304
[12] DOI: 10.1049/ip-cta:20040844
[13] DOI: 10.1016/j.automatica.2006.07.019 · Zbl 1140.93466
[14] DOI: 10.1080/00207729708929455 · Zbl 0886.93047
[15] Du B, in IFAC World Congress 2008 (2008)
[16] Du B, IET Control Theory and Applications
[17] DOI: 10.1007/BFb0027478 · Zbl 0901.00019
[18] DOI: 10.1109/TAC.2006.872828 · Zbl 1366.93482
[19] DOI: 10.1016/j.automatica.2004.03.003 · Zbl 1072.93018
[20] DOI: 10.1109/9.975503 · Zbl 1006.93055
[21] DOI: 10.1109/78.960431 · Zbl 1369.93622
[22] DOI: 10.1109/9.983353 · Zbl 1364.93209
[23] DOI: 10.1109/TAC.2002.804462 · Zbl 1364.93564
[24] DOI: 10.1109/9.995046 · Zbl 1364.93370
[25] DOI: 10.1080/0020717021000049151 · Zbl 1023.93032
[26] DOI: 10.1109/TAC.2002.806674 · Zbl 1364.93797
[27] DOI: 10.1109/TAC.2006.890320 · Zbl 1366.39011
[28] DOI: 10.1049/ip-cta:20040822
[29] DOI: 10.1109/TAC.2003.809154 · Zbl 1364.93211
[30] Gorecki HS, Analysis and Synthesis of Time Delay Systems (1989)
[31] Gouaisbaut F, The 5th IFAC Symposium on Robust Control Design (2006)
[32] Gouaisbaut F, The 5th IFAC Symposium on Robust Control Design (2006)
[33] DOI: 10.1080/002071797223406 · Zbl 0986.93061
[34] DOI: 10.1080/002071799220092 · Zbl 0959.93053
[35] Gu K, Proceedings of 38th IEEE Conference on Decision and Control pp 227– (1999)
[36] Gu K, Proceedings of 39th IEEE Conference on Decision and Control pp 2805– (2000)
[37] Gu K, Kybernetika 37 pp 479– (2001)
[38] DOI: 10.1080/00207170110047190 · Zbl 1015.93053
[39] DOI: 10.1080/00207170010031486 · Zbl 1015.34061
[40] DOI: 10.1007/978-1-4612-0039-0
[41] DOI: 10.1109/9.847747 · Zbl 0986.34066
[42] DOI: 10.1109/9.911431 · Zbl 1056.93511
[43] DOI: 10.1115/1.1569950
[44] DOI: 10.1080/00207720500089317 · Zbl 1075.93031
[45] Halanay A, Differential Equations: Stability, Oscillations, Time Lags (1966)
[46] Hale JK, Theory of Functional Differential Equations (1977)
[47] Hale JK, Introduction to Functional Differential Equations (1993)
[48] DOI: 10.1080/00207720110092207 · Zbl 1031.93138
[49] DOI: 10.1093/imamci/20.4.371 · Zbl 1046.93039
[50] Han Q-L, in Proceedings of American Control Conference pp 5098– (2003)
[51] DOI: 10.1016/j.automatica.2004.05.002 · Zbl 1075.93032
[52] DOI: 10.1016/j.automatica.2005.08.005 · Zbl 1100.93519
[53] DOI: 10.1080/00207720500157437 · Zbl 1093.34037
[54] DOI: 10.1016/j.automatica.2005.08.005 · Zbl 1100.93519
[55] DOI: 10.1016/j.physleta.2006.08.076 · Zbl 1236.93072
[56] DOI: 10.1109/9.948471 · Zbl 1006.93054
[57] DOI: 10.1109/TAC.2003.817006 · Zbl 1364.93593
[58] DOI: 10.1109/TAC.2004.838479 · Zbl 1365.93224
[59] DOI: 10.1016/j.automatica.2006.08.015 · Zbl 1111.93073
[60] DOI: 10.1109/TAC.2004.828317 · Zbl 1365.93368
[61] DOI: 10.1080/002077200291109 · Zbl 1080.93552
[62] DOI: 10.1142/S0218127406014800 · Zbl 1097.94004
[63] DOI: 10.1080/00207729708929488 · Zbl 0899.93031
[64] DOI: 10.1093/imamci/21.2.95 · Zbl 1061.93036
[65] DOI: 10.1016/S0005-1098(02)00227-3 · Zbl 1011.93062
[66] DOI: 10.1016/j.automatica.2005.06.012 · Zbl 1100.93017
[67] DOI: 10.1109/TAC.2004.831109 · Zbl 1365.93226
[68] DOI: 10.1109/9.50357 · Zbl 0707.93060
[69] DOI: 10.1109/TAC.2003.813200 · Zbl 1364.93596
[70] DOI: 10.1109/9.920802 · Zbl 1008.93056
[71] Kolmanovskii VB, Applied Theory of Functional Differential Equations (1992)
[72] Kolmanovskii VB, Introduction to the Theory and Applications of Functional Differential Equations (1999)
[73] DOI: 10.1080/002071799221172 · Zbl 0952.34057
[74] DOI: 10.1109/9.763213 · Zbl 0964.34065
[75] DOI: 10.1109/TSMCB.2006.872262
[76] DOI: 10.1049/ip-cta:20045216
[77] DOI: 10.1016/j.automatica.2003.07.004 · Zbl 1046.93015
[78] DOI: 10.1049/ip-cta:20040641
[79] DOI: 10.1016/S0005-1098(97)00082-4
[80] DOI: 10.1109/9.618244 · Zbl 0889.93050
[81] DOI: 10.1080/00207720118657 · Zbl 1018.34069
[82] DOI: 10.1049/ip-cta:20045124
[83] DOI: 10.1115/1.1540995
[84] DOI: 10.1006/jmaa.2000.6716 · Zbl 0973.34066
[85] DOI: 10.1109/TAC.2005.861720 · Zbl 1366.93469
[86] DOI: 10.1016/j.fss.2005.10.001 · Zbl 1090.93024
[87] DOI: 10.1080/00207720119289 · Zbl 1033.93059
[88] DOI: 10.1049/ip-cta:19990681
[89] DOI: 10.1049/ip-cta:20050223
[90] DOI: 10.1016/j.jmaa.2006.05.041 · Zbl 1132.34061
[91] DOI: 10.1080/0020772031000115489 · Zbl 1060.93077
[92] DOI: 10.1109/TIE.2002.801243
[93] Mahmoud MS, International Journal of Innovative Computing, Information and Control 3 pp 407– (2007)
[94] DOI: 10.1080/00207170110067116 · Zbl 1023.93055
[95] Niculescu S-I, Delay Effects on Stability: A Robust Control Approach (2001)
[96] DOI: 10.1080/00207170010017400 · Zbl 1047.34088
[97] DOI: 10.1109/9.489216 · Zbl 0851.93067
[98] DOI: 10.1016/j.automatica.2004.11.035 · Zbl 1093.93027
[99] DOI: 10.1016/j.camwa.2005.04.003 · Zbl 1093.93009
[100] DOI: 10.1049/ip-cta:20041225
[101] DOI: 10.1016/S0377-0427(00)00583-5 · Zbl 0995.34069
[102] DOI: 10.1016/j.amc.2004.01.001 · Zbl 1077.34075
[103] DOI: 10.1109/9.754838 · Zbl 0957.34069
[104] DOI: 10.1049/ip-cta:20050099
[105] DOI: 10.1016/j.automatica.2006.11.005 · Zbl 1119.93356
[106] DOI: 10.1016/S0005-1098(03)00167-5 · Zbl 1145.93302
[107] DOI: 10.1080/002077200290984 · Zbl 1080.93612
[108] DOI: 10.1243/09596518JSCE287
[109] DOI: 10.1016/j.automatica.2006.06.016 · Zbl 1113.60079
[110] DOI: 10.1080/002077299291723 · Zbl 1033.93507
[111] DOI: 10.1109/9.256406 · Zbl 0770.93077
[112] Sun X-M, International Journal of Innovative Computing Information and Control 3 pp 385– (2007)
[113] DOI: 10.1016/j.amc.2005.12.028 · Zbl 1100.93034
[114] Suplin V, in Proceedings of 43rd IEEE Conference Decision and Control pp 4548– (2004)
[115] DOI: 10.1109/TAC.2006.872767 · Zbl 1366.93163
[116] DOI: 10.1049/ip-cta:20020608
[117] Verriest EI, in Proceedings of 32nd IEEE Conference Decision and Control pp 3473– (1993)
[118] DOI: 10.1080/002077200290876 · Zbl 1080.93635
[119] DOI: 10.1109/TSMCB.2005.862485
[120] DOI: 10.1049/ip-cta:20050296
[121] DOI: 10.1109/TAC.2004.838484 · Zbl 1365.93358
[122] Wu M, International Journal of Control, Automation, and Systems 6 pp 682– (2006)
[123] DOI: 10.1016/j.automatica.2004.03.004 · Zbl 1059.93108
[124] DOI: 10.1016/j.na.2005.08.005 · Zbl 1161.93315
[125] DOI: 10.1109/TAC.2005.843873 · Zbl 1365.93376
[126] DOI: 10.1109/TAC.2006.886495 · Zbl 1366.93451
[127] DOI: 10.1109/TSP.2005.855109 · Zbl 1370.93109
[128] DOI: 10.1016/j.cam.2004.12.025 · Zbl 1097.34057
[129] DOI: 10.1111/j.1934-6093.2005.tb00404.x
[130] DOI: 10.1080/0020772031000071785 · Zbl 1063.34068
[131] DOI: 10.1111/j.1934-6093.2005.tb00244.x
[132] DOI: 10.1049/ip-cta:20045023
[133] DOI: 10.1049/ip-cta:20045191
[134] DOI: 10.1016/j.automatica.2005.09.013 · Zbl 1099.93010
[135] DOI: 10.1109/TAC.2002.800651 · Zbl 1364.93723
[136] DOI: 10.1016/j.fss.2006.09.004 · Zbl 1110.93033
[137] Yu L, Proceedings of 42nd IEEE Conference Decision and Control pp 6033– (2003)
[138] Yue D, in Proceedings of American Control Conference pp 5438– (2004)
[139] DOI: 10.1109/TAC.2004.841935 · Zbl 1365.93377
[140] DOI: 10.1049/ip-cta:20045293
[141] DOI: 10.1016/j.automatica.2005.03.009 · Zbl 1093.93024
[142] Zhao Y, IEEE Transactions on Fuzzy Systems (2008)
[143] DOI: 10.1016/S0005-1098(01)00232-1 · Zbl 0995.93065
[144] DOI: 10.1016/j.fss.2004.08.014 · Zbl 1142.93379
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