A study on decentralized H ∞ feedback control systems with local quantizers

Guisheng Zhai; Ning Chen; Weihua Gui

Kybernetika (2009)

  • Volume: 45, Issue: 1, page 137-150
  • ISSN: 0023-5954

Abstract

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In this paper, we study decentralized H ∞ 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 ∞ 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 ∞ disturbance attenuation level. We also extend the discussion and the result to the case of multi-channel discrete-time H ∞ feedback control systems.

How to cite

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Zhai, Guisheng, Chen, Ning, and Gui, Weihua. "A study on decentralized $H_\infty $ feedback control systems with local quantizers." Kybernetika 45.1 (2009): 137-150. <http://eudml.org/doc/37665>.

@article{Zhai2009,
abstract = {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.},
author = {Zhai, Guisheng, Chen, Ning, Gui, Weihua},
journal = {Kybernetika},
keywords = {decentralized $H_\{\infty \}$ feedback control system; quantizer; quantization; matrix inequality; output feedback; decentralized feedback control system; quantizer; quantization; matrix inequality; output feedback},
language = {eng},
number = {1},
pages = {137-150},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A study on decentralized $H_\infty $ feedback control systems with local quantizers},
url = {http://eudml.org/doc/37665},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Zhai, Guisheng
AU - Chen, Ning
AU - Gui, Weihua
TI - A study on decentralized $H_\infty $ feedback control systems with local quantizers
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 1
SP - 137
EP - 150
AB - 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.
LA - eng
KW - decentralized $H_{\infty }$ feedback control system; quantizer; quantization; matrix inequality; output feedback; decentralized feedback control system; quantizer; quantization; matrix inequality; output feedback
UR - http://eudml.org/doc/37665
ER -

References

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  2. Special section on networks & control, IEEE Control Systems Magazine 21 (2001), 22–99. 
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  5. A Unified Algebraic Approach to Linear Control Design, Taylor & Francis, London 1998. MR1484416
  6. Nonlinear stabilization by hybrid quantized feedback, In: Proc. 3rd Internat. Workshop on Hybrid Systems: Computation and Control, Pittsburgh 2000, pp. 243–257. Zbl0952.93109
  7. Hybrid feedback stabilization of systems with quantized signals, Automatica 39 (2003), 1543–1554. Zbl1030.93042MR2143462
  8. 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. 
  9. Hybrid stabilization of linear time-invariant systems with two quantizers, In: Proc. 2004 IEEE Internat. Symposium on Intelligent Control, Taipei 2004, pp. 305–309. 
  10. Design of H ∞ feedback control systems with quantized signals, In: Preprints of the 16th IFAC World Congress, Paper code: Fr-M17-TO/1, Prague 2005. 

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