Decentralized design of interconnected H∞ feedback control systems with quantized signals
Guisheng Zhai ; Ning Chen ; Weihua Gui
International Journal of Applied Mathematics and Computer Science, Tome 23 (2013), p. 317-325 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

In this paper, we consider the design of interconnected H∞ feedback control systems with quantized signals. We assume that a decentralized dynamic output feedback has been designed for an interconnected continuous-time LTI system so that the closed-loop system is stable and a desired H∞ disturbance attenuation level is achieved, and that the subsystem measurement outputs are quantized before they are passed to the local controllers. We propose a local-output-dependent strategy for updating the parameters of the quantizers, so that the overall closed-loop system is asymptotically stable and achieves the same H∞ disturbance attenuation level. Both the pre-designed controllers and the parameters of the quantizers are constructed in a decentralized manner, depending on local measurement outputs.

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:257112 
@article{bwmeta1.element.bwnjournal-article-amcv23z2p317bwm,
     author = {Guisheng Zhai and Ning Chen and Weihua Gui},
     title = {Decentralized design of interconnected $H\_$\infty$$ feedback control systems with quantized signals},
     journal = {International Journal of Applied Mathematics and Computer Science},
     volume = {23},
     year = {2013},
     pages = {317-325},
     zbl = {1282.93105},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv23z2p317bwm}
}

Guisheng Zhai; Ning Chen; Weihua Gui. Decentralized design of interconnected $H_∞$ feedback control systems with quantized signals. International Journal of Applied Mathematics and Computer Science, Tome 23 (2013) pp. 317-325. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv23z2p317bwm/

[000] Brockett, R.W. and Liberzon, D. (2000). Quantized feedback stabilization of linear systems, IEEE Transactions on Automatic Control 45(7): 1279-1289. | Zbl 0988.93069

[001] Bushnell, L.G. (2001). Special section on networks & control, IEEE Control Systems Magazine 21(1): 22-99.

[002] Chen, N., Shen, X. and Gui, W. (2011a). Decentralized H∞ quantized dynamic output feedback control for uncertain interconnected networked systems, Proceedings of the 8th Asian Control Conference, Kaohsiung, Taiwan, pp. 131-136.

[003] Chen, W., Khan, A.Q., Abid, M. and Ding, S.X. (2011b). Integrated design of observer based fault detection for a class of uncertain nonlinear systems, International Journal of Applied Mathematics and Computer Science 21(3): 423-430, DOI: 10.2478/v10006-011-0031-0. | Zbl 1234.93036

[004] Delchamps, D.F. (1990). Stabilizing a linear system with quantized state feedback, IEEE Transactions on Automatic Control 35(8): 916-924. | Zbl 0719.93067

[005] Ikeda, M., Zhai, G. and Fujisaki, Y. (1996). Decentralized H∞ control for large-scale systems: A matrix inequality approach using a homotopy method, Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan, pp. 1-6.

[006] Ishii, H. and Francis, B. (2002). Limited Data Rate in Control Systems with Networks, Springer, Berlin. | Zbl 1001.93001

[007] Iwasaki, T., Skelton, R.E. and Grigoriadis, K.M. (1998). A Unified Algebraic Approach to Linear Control Design, Taylor & Francis, London.

[008] Liberzon, D. (2000). Nonlinear stabilization by hybrid quantized feedback, Proceedings of the 3rd International Workshop on Hybrid Systems: Computation and Control, Pittsburgh, PA, USA, pp. 243-257. | Zbl 0952.93109

[009] Liberzon, D. (2003). Hybrid feedback stabilization of systems with quantized signals, Automatica 39(9): 1543-1554. | Zbl 1030.93042

[010] Ling, Q. and Lemmon, M.D. (2010). A necessary and sufficient feedback dropout condition to stabilize quantized linear control systems with bounded noise, IEEE Transactions on Automatic Control 55(11): 2590-2596.

[011] Morawski, M. and Zajączkowski, A.M. (2010). Approach to the design of robust networked control systems, International Journal of Applied Mathematics and Computer Science 20(4): 689-698, DOI: 10.2478/v10006-010-0052-0.

[012] Murao, S., Zhai, G., Ikeda, M. and Tamaoki, K. (2002). Decentralized H∞ controller design: An LMI approach, Proceedings of the 41st SICE Annual Conference, Osaka, Japan, pp. 2734-2739.

[013] Tatikonda, S. and Mitter, S. (2004). Control under communication constraints, IEEE Transactions on Automatic Control 49(7): 1056-1068.

[014] Zhai, G., Chen, N. and Gui, W. (2010). Quantizer design for interconnected feedback control systems, Journal of Control Theory and Applications 8(1): 93-98.

[015] Zhai, G., Ikeda, M. and Fujisaki, Y. (2001). Decentralized H∞ controller design: A matrix inequality approach using a homotopy method, Automatica 37(4): 565-572. | Zbl 0982.93035

[016] Zhai, G., Matsumoto, Y., Chen, X. and Mi, Y. (2004). Hybrid stabilization of linear time-invariant systems with two quantizers, Proceedings of the 2004 IEEE International Symposium on Intelligent Control, Taipei, Taiwan, pp. 305-309.

[017] Zhai, G., Mi, Y., Imae, J. and Kobayashi, T. (2005). Design of H∞ feedback control systems with quantized signals, Preprints of the 16th IFAC World Congress, Prague, Czech Republic, Fr-M17-TO/1.