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Absolute stability and stabilization for Lurie networked control systems. (Absolute stability and stabilization for Lur’e networked control systems.) (English) Zbl 1227.93099

Summary: This paper investigates the problem of absolute stability and stabilization for Networked Control Systems (NCSs) with the controlled plant being a Lur’e system (Lur’e NCS), in which the network-induced delays are assumed to be time-varying and bounded. By considering the relationship between the network-induced delay and its upper bound, an improved stability criterion for networked control system is proposed. Furthermore, the resulting condition is extended to design a state feedback controller by employing an Improved Cone Complementary Linearization (ICCL) algorithm. A numerical example is worked out to illustrate the effectiveness and the benefits of the proposed method.

MSC:

93D15 Stabilization of systems by feedback
93B18 Linearizations
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[1] Lee, Worst case communication delay of real-time industrial switched ethernet with multiple levels, IEEE Transactions on Industrial Electronics 53 pp 1669– (2006) · doi:10.1109/TIE.2006.881986
[2] Tang, Improvement of state feedback controller design for networked control systems, IEEE Transactions on Circuits and Systems II: Express Briefs 55 (5) pp 464– (2008) · doi:10.1109/TCSII.2007.914893
[3] Walsh, Stability analysis of networked control systems, IEEE Transactions on Control Systems Technology 10 (3) pp 438– (2002) · doi:10.1109/87.998034
[4] Yang, H control for networked systems with random communication delays, IEEE Transactions on Automatic Control 51 (3) pp 511– (2006) · Zbl 1366.93167 · doi:10.1109/TAC.2005.864207
[5] Yang, Networked control systems: a brief survey, IEE Proceedings of Control Theory and Application 153 (4) pp 403– (2006) · doi:10.1049/ip-cta:20050178
[6] Zhang, Stability of networked control systems, IEEE Control Systems Magazine 21 pp 84– (2001) · doi:10.1109/37.898794
[7] Wang, H control of networked control systems via LMI approach, International Journal of Innovative Computing, Information and Control 3 pp 343– (2007) · doi:10.1109/ICICIC.2007.239
[8] Peng, State feedback controller design of networked control systems with interval time-varying delay and nonlinearity, International Journal of Robust and Nonlinear Control 18 (12) pp 1285– (2008) · Zbl 1284.93111 · doi:10.1002/rnc.1278
[9] Gao, A new delay system approach to network-based control, Automatica 44 (1) pp 39– (2008) · Zbl 1138.93375 · doi:10.1016/j.automatica.2007.04.020
[10] Kim, Maximum allowable delay bounds of networked control systems, Control Engineering Practice 11 (11) pp 1301– (2003) · doi:10.1016/S0967-0661(02)00238-1
[11] Boukas, Delay-dependent stabilization of singular linear systems with delays, International Journal of Innovative Computing, Information and Control 2 pp 283– (2006)
[12] Fridman, Delay-dependent stability and H control: constant and time-varying delays, International Journal of Control 76 pp 48– (2003) · Zbl 1023.93032 · doi:10.1080/0020717021000049151
[13] Gao, Delay-dependent output-feedback stabilisation of discrete-time systems with time-varying state delay, IEE Proceedings of Control Theory and Application 151 (6) pp 691– (2004) · doi:10.1049/ip-cta:20040822
[14] Gu, Stability of Time-Delay Systems (2003) · Zbl 1039.34067 · doi:10.1007/978-1-4612-0039-0
[15] Jiang, On H control for linear systems with interval time-varying delay, Automatica 41 (12) pp 2099– (2005) · Zbl 1100.93017 · doi:10.1016/j.automatica.2005.06.012
[16] Lin, A less conservative robust stability test for linear uncertain time-delay systems, IEEE Transactions on Automatic Control 51 (1) pp 87– (2006) · Zbl 1366.93469 · doi:10.1109/TAC.2005.861720
[17] Zhang, Delay-dependent stabilization of linear systems with time-varying state and input delays, Automatica 41 (8) pp 1405– (2005) · Zbl 1093.93024 · doi:10.1016/j.automatica.2005.03.009
[18] He, Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays, Systems and Control Letters 51 (1) pp 57– (2004) · Zbl 1157.93467 · doi:10.1016/S0167-6911(03)00207-X
[19] Moon, Delay-dependent robust stabilization of uncertain state-delayed systems, International Journal of Control 74 (14) pp 1447– (2001) · Zbl 1023.93055 · doi:10.1080/00207170110067116
[20] He, Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties, IEEE Transactions on Automatic Control 49 (5) pp 828– (2004) · Zbl 1365.93368 · doi:10.1109/TAC.2004.828317
[21] Wu, Delay-dependent criteria for robust stability of time-varying delay systems, Automatica 40 (8) pp 1435– (2004) · Zbl 1059.93108 · doi:10.1016/j.automatica.2004.03.004
[22] Yue, State feedback controller design of networked control systems, IEEE Transactions on Circuits and Systems, Part II 51 (11) pp 640– (2004) · doi:10.1109/TCSII.2004.836043
[23] Wu, New delay-dependent stability criteria and stabilizing method for neutral systems, IEEE Transactions on Automatic Control 49 (12) pp 2266– (2004) · Zbl 1365.93358 · doi:10.1109/TAC.2004.838484
[24] Yue, Network-based robust H control of systems with uncertainty, Automatica 41 (6) pp 999– (2005) · Zbl 1091.93007 · doi:10.1016/j.automatica.2004.12.011
[25] He, Improved stabilisation method for networked control systems, IET Control Theory and Applications 1 (6) pp 1580– (2007) · doi:10.1049/iet-cta:20070015
[26] Hao, Absolute stability of Lurie networked control systems, International Journal of Robust and Nonlinear Control 20 (12) pp 1326– (2010) · Zbl 1206.93103
[27] Ghaoui, A cone complementarity linearization algorithm for static output-feedback and related problems, IEEE Transactions on Automatic Control 42 pp 1171– (1997) · Zbl 0887.93017 · doi:10.1109/9.618250
[28] Khalil, Nonlinear Systems (1996)
[29] Jiang, New stability criteria for linear systems with interval time-varying delay, Automatica 44 (10) pp 2680– (2008) · Zbl 1155.93405 · doi:10.1016/j.automatica.2008.02.020
[30] Boyd, Linear Matrix Inequality in System and Control Theory (1994) · Zbl 0816.93004 · doi:10.1137/1.9781611970777
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