×

Robust partially mode delay dependent \(\mathcal{H}_{\infty}\) control of discrete-time networked control systems. (English) Zbl 1307.93138

Summary: This article proposes a methodology for designing a partially mode delay dependent \(\mathcal{H}_{\infty}\) controller design for discrete-time systems with random communication delays. Communication delays between sensors and controller are modelled by a finite state Markov chain where the transition probability matrix is partially known. Stability criteria are obtained based on Lyapunov-Krasovskii functional and a novel methodology for designing a partially mode delay dependent state feedback controller has been proposed. The controller is obtained by solving linear matrix inequality optimisation problems using cone complimentarity linearisation algorithm. A numerical example is provided to illustrate the effectiveness of the proposed controller.

MSC:

93B36 \(H^\infty\)-control
93B35 Sensitivity (robustness)
93C55 Discrete-time control/observation systems
93A15 Large-scale systems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1023/A:1017515721760 · Zbl 0988.93062 · doi:10.1023/A:1017515721760
[2] DOI: 10.1080/10241230212910 · Zbl 1060.93101 · doi:10.1080/10241230212910
[3] DOI: 10.1109/MCS.2001.898789 · doi:10.1109/MCS.2001.898789
[4] Cao YY, Journal of The Franklin Institute 45 pp 423– (2000)
[5] DOI: 10.1049/iet-cta.2009.0096 · doi:10.1049/iet-cta.2009.0096
[6] Chen, WH and Zheng, WX. 2007. Robust Stabilization of Delayed Markovian Jump Systems Subject to Parametric Uncertainties. Proceedings of the 46th IEEE Conference on Decision and Control. 2007. pp.3054–3059. New Orleans, LA, USA · doi:10.1109/CDC.2007.4434107
[7] DOI: 10.1109/9.618250 · Zbl 0887.93017 · doi:10.1109/9.618250
[8] DOI: 10.1109/CHICC.2006.280653 · doi:10.1109/CHICC.2006.280653
[9] DOI: 10.1080/00207720500089317 · Zbl 1075.93031 · doi:10.1080/00207720500089317
[10] DOI: 10.1007/978-1-4684-4841-2 · doi:10.1007/978-1-4684-4841-2
[11] DOI: 10.1016/j.automatica.2006.12.020 · Zbl 1123.93075 · doi:10.1016/j.automatica.2006.12.020
[12] DOI: 10.1109/TAC.2008.919571 · Zbl 1367.93510 · doi:10.1109/TAC.2008.919571
[13] DOI: 10.1016/S0167-6911(01)00132-3 · Zbl 0986.93075 · doi:10.1016/S0167-6911(01)00132-3
[14] DOI: 10.1109/ICIEA.2007.4318780 · doi:10.1109/ICIEA.2007.4318780
[15] Nilsson J, Ph.D. Dissertation (1998)
[16] DOI: 10.1016/j.compchemeng.2003.09.027 · doi:10.1016/j.compchemeng.2003.09.027
[17] DOI: 10.1109/TCSII.2004.825596 · doi:10.1109/TCSII.2004.825596
[18] Wang Y, 8th Control, Automation, Robotics and Vision Conference 1 pp 298– (2004)
[19] DOI: 10.1109/81.974887 · doi:10.1109/81.974887
[20] DOI: 10.1016/j.sigpro.2009.07.020 · Zbl 1177.93086 · doi:10.1016/j.sigpro.2009.07.020
[21] DOI: 10.1109/TCSII.2007.894413 · doi:10.1109/TCSII.2007.894413
[22] DOI: 10.1109/TAC.2005.864207 · Zbl 1366.93167 · doi:10.1109/TAC.2005.864207
[23] DOI: 10.1109/TAC.2008.2007867 · Zbl 1367.93710 · doi:10.1109/TAC.2008.2007867
[24] DOI: 10.1109/37.898794 · doi:10.1109/37.898794
[25] DOI: 10.1002/acs.901 · Zbl 1127.93324 · doi:10.1002/acs.901
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.