# Article

 Title: A study on decentralized $H_\infty$ feedback control systems with local quantizers (English) Author: Zhai, Guisheng Author: Chen, Ning Author: Gui, Weihua Language: English Journal: Kybernetika ISSN: 0023-5954 Volume: 45 Issue: 1 Year: 2009 Pages: 137-150 Summary lang: English . Category: math . Summary: In this paper, we study decentralized $H_{\infty}$ feedback control systems with quantized signals in local input-output (control) channels. We first assume that a decentralized output feedback controller has been designed for a multi-channel continuous-time system so that the closed-loop system is Hurwitz stable and a desired $H_{\infty}$ disturbance attenuation level is achieved. However, since the local measurement outputs are quantized by a general quantizer before they are passed to the controller, the system's performance is not guaranteed. For this reason, we propose a local-output-dependent strategy for updating the quantizers' parameters, so that the closed-loop system is asymptotically stable and achieves the same $H_{\infty}$ disturbance attenuation level. We also extend the discussion and the result to the case of multi-channel discrete-time $H_{\infty}$ feedback control systems. (English) Keyword: decentralized $H_{\infty}$ feedback control system Keyword: quantizer Keyword: quantization Keyword: matrix inequality Keyword: output feedback MSC: 93A14 MSC: 93B36 MSC: 93C15 MSC: 93C55 MSC: 93C83 MSC: 93D15 MSC: 93D25 idZBL: Zbl 1158.93350 idMR: MR2489585 . Date available: 2010-06-02T18:23:53Z Last updated: 2012-06-06 Stable URL: http://hdl.handle.net/10338.dmlcz/140007 . Reference: [1] R. W. Brockett and D. Liberzon: Quantized feedback stabilization of linear systems.IEEE Trans. Automat. Control 45 (2000), 1279–1289. MR 1779982 Reference: [2] L. G. Bushnell: Special section on networks & control.IEEE Control Systems Magazine 21 (2001), 22–99. Reference: [3] D. F. Delchamps: Stabilizing a linear system with quantized state feedback.IEEE Trans. Automat. Control 35 (1990), 916–924. Zbl 0719.93067, MR 1064642 Reference: [4] H. Ishii and B. Francis: Limited Data Rate in Control Systems with Networks.Springer-Verlag, Berlin 2002. MR 1898626 Reference: [5] T. Iwasaki, R. E. Skelton, and K. M. Grigoriadis: A Unified Algebraic Approach to Linear Control Design.Taylor & Francis, London 1998. MR 1484416 Reference: [6] D. Liberzon: Nonlinear stabilization by hybrid quantized feedback.In: Proc. 3rd Internat. Workshop on Hybrid Systems: Computation and Control, Pittsburgh 2000, pp. 243–257. Zbl 0952.93109 Reference: [7] D. Liberzon: Hybrid feedback stabilization of systems with quantized signals.Automatica 39 (2003), 1543–1554. Zbl 1030.93042, MR 2143462 Reference: [8] Y. Matsumoto, G. Zhai, and Y. Mi: Stabilization of discrete-time LTI systems by hybrid quantized output feedback.In: Preprints of the 46th Japan Joint Automatic Control Conference, Okayama 2003, pp. 799–802. Reference: [9] H. Zhai, Y. Matsumoto, X. Chen, and Y. Mi: Hybrid stabilization of linear time-invariant systems with two quantizers.In: Proc. 2004 IEEE Internat. Symposium on Intelligent Control, Taipei 2004, pp. 305–309. Reference: [10] G. Zhai, Y. Mi, J. Imae, and T. Kobayashi: Design of ${{H}}_{\infty }$ feedback control systems with quantized signals.In: Preprints of the 16th IFAC World Congress, Paper code: Fr-M17-TO/1, Prague 2005. .

## Files

Files Size Format View
Kybernetika_45-2009-1_10.pdf 1.043Mb application/pdf View/Open

Partner of