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Integral partitioning approach to robust stabilization for uncertain distributed time-delay systems. (English) Zbl 1273.93140
Summary: In this paper, the problems of robust delay-dependent stability analysis and stabilization are investigated for distributed delay systems with linear fractional uncertainties. By introducing an integral partitioning technique, a new form of Lyapunov functional is constructed and improved distributed delay-dependent stability conditions are established in terms of linear matrix inequalities. Based on the criterion, a design algorithm for a state-feedback controller is proposed. Following similar lines, we extend these results to uncertain distributed delay systems. The results developed in this paper can tolerate larger allowable delay than existing ones in the literature, which is illustrated by several examples.

MSC:
93D21 Adaptive or robust stabilization
93B52 Feedback control
93B40 Computational methods in systems theory (MSC2010)
93C15 Control/observation systems governed by ordinary differential equations
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[1] Dugard, Stability and Control of Time-delay Systems (1998) · Zbl 0901.00019 · doi:10.1007/BFb0027478
[2] Li, Delay-dependent robust stability and stabilization of uncertain linear delay system: a linear matrix ineqality approach, IEEE Transactions on Automatic Control 42 pp 1144– (1997) · Zbl 0889.93050 · doi:10.1109/9.618244
[3] Gao, A new delay system approach to network based control, Automatica 44 pp 39– (2008) · Zbl 1138.93375 · doi:10.1016/j.automatica.2007.04.020
[4] Wang, H filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities, Automatica 44 pp 1268– (2008) · Zbl 1283.93284 · doi:10.1016/j.automatica.2007.09.016
[5] Xu, A survey of linear matrix inequality techniques in stability analysis of delay systems, International Journal of Systems Science 39 pp 1095– (2008) · Zbl 1156.93382 · doi:10.1080/00207720802300370
[6] Moon, Delay-dependent robust stabilization of uncertain state-delayed systems, International Journal of Control 74 pp 1447– (2001) · Zbl 1023.93055 · doi:10.1080/00207170110067116
[7] Xu, Improved delay-dependent stability criteria for time-delay systems, IEEE Transactions on Automatic Control 50 pp 384– (2005) · Zbl 1365.93376 · doi:10.1109/TAC.2005.843873
[8] Gouaisbaut F Peaucelle D Delay-dependent stability analysis of linear time delay systems · Zbl 1293.93589
[9] He, Delay-range-dependent stability for systems with time-varying delay, Automatica 43 pp 371– (2007) · Zbl 1111.93073 · doi:10.1016/j.automatica.2006.08.015
[10] Jiang, New stability criteria for linear systems with interval time-varying delay, Automatica 44 pp 2680– (2008) · Zbl 1155.93405 · doi:10.1016/j.automatica.2008.02.020
[11] Shao, New delay-dependent criteria for systems with interval delay, Automatica 45 pp 744– (2009) · Zbl 1168.93387 · doi:10.1016/j.automatica.2008.09.010
[12] Fridman, New conditions for delay-derivative-dependent stability, Automatica 45 pp 2723– (2009) · Zbl 1180.93080 · doi:10.1016/j.automatica.2009.08.002
[13] Xu, An LMI approach to the H filter design for uncertain systems with distributed delays, IEEE Transactions on Circuits and Systems (II) 51 pp 195– (2004) · doi:10.1109/TCSII.2003.822432
[14] Fiagbedzi, A multistage reduction technique for feedback stabilizing distributed time-lag systems, Automatica 23 pp 311– (1987) · Zbl 0629.93046 · doi:10.1016/0005-1098(87)90005-7
[15] Li, Mean square exponential stability of stochastic fuzzy hopfield neural networks with discrete and distributed time-varying delays, Neurocomputing 72 pp 2017– (2009) · Zbl 05719005 · doi:10.1016/j.neucom.2008.12.006
[16] Li, Robust exponential stability for uncertain stochastic neural networks with discrete and distributed time-varying delays, Physics Letter A 372 pp 3385– (2008) · Zbl 1220.82085 · doi:10.1016/j.physleta.2008.01.060
[17] Yue, Delay-dependent robust H controller design for uncertain descriptor systems with time-varying discrete and distributed delays, IEE Proceedings Control Theory and Applications 152 pp 628– (2005) · doi:10.1049/ip-cta:20045293
[18] Xie, Robust H control of distributed delay systems with application to combustion control, IEEE Transactions on Automatic Control 46 pp 1930– (2001) · Zbl 1017.93038 · doi:10.1109/9.975483
[19] Fridman, H control of distributed and discrete delay systems via discretized Lyapunov functional, European Journal of Control 1 pp 1– (2009) · Zbl 1298.93149
[20] Wu, Robust H control of uncertain distributed delay systems: parameter-dependent Lyapunov functional approach, Dynamics of Continuous Discrete and Impulsive Systems: Series B-Applications and Algorithms 14 pp 155– (2007)
[21] Xu, A delay-dependent approach to robust H filtering for uncertain distributed delay systems, IEEE Transactions on Signal Processing 53 pp 3764– (2005) · Zbl 1370.93109 · doi:10.1109/TSP.2005.855109
[22] Yue, Robust H filter design of uncertain descriptor systems with discrete and distributed delays, IEEE Transactions on Signal Processing 52 pp 3200– (2004) · Zbl 1370.93111 · doi:10.1109/TSP.2004.836535
[23] Wu, Delay-dependent robust H and L2 - L filtering for LPV systems with both discrete and distributed delays, IEE Proceedings Control Theory and Applications 153 pp 483– (2006) · doi:10.1049/ip-cta:20050296
[24] Zheng, Robust control of uncertain distributed delay systems with application to the stabilization of combustion in rocket motor chambers, Automatica 38 (2) pp 487– (2002) · Zbl 0995.93065 · doi:10.1016/S0005-1098(01)00232-1
[25] Gu, An improved stability criterion for systems with distributed delays, International Journal of Robust and Nonlinear Control 13 pp 819– (2003) · Zbl 1039.93031 · doi:10.1002/rnc.847
[26] Suh, Stability condition of distributed delay systems based on an analytic solution to Lyapunov functional equations, Asian Journal of Control 8 pp 91– (2006) · doi:10.1111/j.1934-6093.2006.tb00258.x
[27] Chen, Delay-dependent robust stabilization for uncertain neutral systems with distributed delays, Automatica 43 pp 95– (2007) · Zbl 1140.93466 · doi:10.1016/j.automatica.2006.07.019
[28] Fridman, New Lyapunov-Krasovkii functionals for stability of linear retarded and neutral type systems, Systems and Control Letters 43 pp 309– (2001) · Zbl 0974.93028 · doi:10.1016/S0167-6911(01)00114-1
[29] Li, Stability analysis of neutral systems with distributed delays, Automatica 44 pp 2197– (2008) · Zbl 1283.93212 · doi:10.1016/j.automatica.2007.12.009
[30] Sun J Chen J Liu G Rees D On robust stability of uncertain neutral systems with discrete and distributed delays 5469 5473
[31] Gu K An integral inequality in the stability problem of time-delay systems 2805 2810
[32] Li, Robust stability for neural networks with time-varying delays and linear fractional uncertainties, Neurocomputing 71 pp 421– (2007) · Zbl 05716325 · doi:10.1016/j.neucom.2007.08.012
[33] Balasubramaniam, Delay-interval dependent robust stability criteria for stochastic neural networks with linear fractional uncertainties, Neurocomputing 72 pp 3675– (2009) · Zbl 05721155 · doi:10.1016/j.neucom.2009.06.006
[34] Zhou, Robust stabilization of delayed singular systems with linear fractional parametric uncertainties, Circuits, Systems and Signal Processing 22 pp 579– (2003) · Zbl 1045.93042 · doi:10.1007/s00034-003-1218-x
[35] Wu, Delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays, Journal of Control Theory and Applications 6 pp 171– (2008) · doi:10.1007/s11768-008-6166-3
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