| 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. |
| . |
