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Equivalence of stability criteria for time-delay
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| Haiyun AN,Hongjie JIA,Yuan ZENG,Wei WEI, |
| Key Laboratory of Power
System Simulation and Control of Ministry of Education, Tianjin University,
Tianjin 300072, China; |
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Abstract During the past few decades, there have been a number of new delay-dependent stability criteria based on linear matrix inequalities published in the literature. These criteria, to some extent, can reduce the conservativeness. In fact, some criteria are equivalence. In this paper, we aim to theoretically establish equivalence of two stability criteria. One was obtained by Sun et al. [Sun et al. In: Proceedings of IEEE Power & Energy Society General Meeting. 2009, 1–7] and the other was given by Xu et al. [Xu et al. IEEE Transactions on Automatic Control, 2005, 50(3): 384–387]. Also, we theoretically establish equivalence of the robust stability criterion presented by Jia et al. [Jia et al. Automation of Electric Power Systems, 2010, 34(3): 6–11] and the one given by Xu et al. (2005).
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| Keywords
delay-dependent stability criterion
robust stability
time-delay systems
linear matrix inequality (LMI)
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Issue Date: 05 June 2010
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Jiang X F, Han Q L. Delay-dependent robust stability for uncertain linear systems with interval time-varyingdelay. Automatica, 2006, 42(6): 1059–1065
doi: 10.1016/j.automatica.2006.02.019
|
|
Han Q L, Yue D. Absolute stability of Lur’e systems with time-varying delay. IET Proceedings: Control Theory & Applications, 2007, 1(3): 854–859
|
|
He Y, Wu M, She J H. Delay-dependent exponential stabilityof delayed neural networks with time-varying delay. IEEE Transactions on Circuits and Systems II: Express Briefs, 2006, 53(7): 553–557
doi: 10.1109/TCSII.2006.876385
|
|
He Y, Wang Q G, Xie L H, Lin C. Further improvement of free-weighting matrices technique for systems withtime-varying delay. IEEE Transactions onAutomatic Control, 2007, 52(2): 293–299
doi: 10.1109/TAC.2006.887907
|
|
Xu S Y, Lam J, Mao X R. Delay-dependent H∞ controland filtering for uncertain Markovian jump system with time-varyingdelay. IEEE Transactions on Circuits and Systems I: RegularPapers, 2007, 54(9): 2070–2077
doi: 10.1109/TCSI.2007.904640
|
|
Yu K W, Lien C H. Stability criteria for uncertain neutral systems with interval time-varyingdelays. Chaos, Solitons and Fractals, 2008, 38(3): 650–657
doi: 10.1016/j.chaos.2007.01.002
|
|
Yu J J, Zhang K J, Fei S M. Further results on mean square exponentialstability of uncertain stochastic delayed neural networks. Communications in Nonlinear Science and NumericalSimulation, 2009, 14(4): 1582–1589
doi: 10.1016/j.cnsns.2008.04.009
|
|
Zhang Y, He Y, Wu M. Delay-dependent robust stability for uncertain stochasticsystems with interval time-varying delay. Acta Automatica Sinica, 2009, 35(5): 577–582
|
|
He Y, Wang Q G, Lin C, Wu M. Delay-range-dependent stability for systems with time-varying delay. Automatica, 2007, 43(2): 371– 376
doi: 10.1016/j.automatica.2006.08.015
|
|
Xu S Y, Lam J. Improved delay-dependent stability criteria for time-delay systems. IEEE Transactions on Automatic Control, 2005, 50(3): 384–387
doi: 10.1109/TAC.2005.843873
|
|
Xu S, Lam J, Zou Y. Simplified descriptor system approachto delay-dependent stability and performance analyses for time-delaysystems. IEE Proceedings — ControlTheory and Applications, 2005, 152(2): 147–151
doi: 10.1049/ip-cta:20045023
|
|
Fridman E, Shaked U. A descriptor system approach to H∞ control of linear time-delay systems. IEEE Transactions on Automatic Control, 2002, 47(2): 253–270
doi: 10.1109/9.983353
|
|
Sun Q, An H Y, Jia H J, Yu X D, Wang C S, Wei W, Ma Z Y, Zeng Y, Zhao J L, Li P. An improved power systemstability criterion with multiple time delays. In: Proceedings of IEEE Power & Energy Society General Meeting. 2009, 1–7
|
|
Gau R S, Lien C H, Hsieh J G. Global exponential stability for uncertaincellular neural networks with multiple time-varying delays via LMIapproach. Chaos, Solitons and Fractals, 2007, 32(4): 1258–1267
doi: 10.1016/j.chaos.2005.11.036
|
|
Zhang J H, Shi P, Qiu J Q. Novel robust stability criteria for uncertainstochastic Hopfield neural networks with time-varying delays. Nonlinear Analysis: Real World Applications, 2007, 8(4): 1349–1357
doi: 10.1016/j.nonrwa.2006.06.010
|
|
Zhang B Y, Xu S Y, Li Y M, Chu Y M. On global exponential stability of high-order neural networks withtime-varying delays. Physics Letters A, 2007, 366(1–2): 69–78
doi: 10.1016/j.physleta.2007.01.065
|
|
Luo M Z, Zhong S M, Wang R J, Kang W. Robust stability analysis for discrete-time stochastic neural networks systemswith time-varying delays. Applied Mathematics and Computation, 2009, 209(2): 305–313
doi: 10.1016/j.amc.2008.12.084
|
|
Shao H Y. Improved delay-dependent stability criteria for systemswith a delay varying in a range. Automatica, 2008, 44(12): 3215–3218
doi: 10.1016/j.automatica.2008.09.003
|
|
He Y, Wu M, She J H. Delay-dependent stability criteria forlinear systems with multiple time delays. IEE Proceedings — Control Theory and Applications, 2006, 153(4): 447–452
doi: 10.1049/ip-cta:20045279
|
|
Jia H J, An H Y, Yu X D. A delay-dependent robuststability criterion for power system and its application. Automation of Electric Power Systems, 2010, 34(3): 6–11 (in Chinese)
|
|
Lee Y S, Moon Y S, Kwon W H, Park P G. Delay-dependent robust H∞ control for uncertain systems with a state-delay. Automatica, 2004, 40(1): 65–72
doi: 10.1016/j.automatica.2003.07.004
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