Hybrid stabilization of discrete-time LTI systems with two quantized signals

Guisheng Zhai; Yuuki Matsumoto; Xinkai Chen; Joe Imae; Tomoaki Kobayashi

International Journal of Applied Mathematics and Computer Science (2005)

  • Volume: 15, Issue: 4, page 509-516
  • ISSN: 1641-876X

Abstract

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We consider stabilizing a discrete-time LTI (linear time-invariant) system via state feedback where both the quantized state and control input signals are involved. The system under consideration is stabilizable and stabilizing state feedback has been designed without considering quantization, but the system's stability is not guaranteed due to the quantization effect. For this reason, we propose a hybrid quantized state feedback strategy asymptotically stabilizing the system, where the values of the quantizer parameters are updated at discrete time instants. We also extend the result to the case of static output feedback.

How to cite

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Zhai, Guisheng, et al. "Hybrid stabilization of discrete-time LTI systems with two quantized signals." International Journal of Applied Mathematics and Computer Science 15.4 (2005): 509-516. <http://eudml.org/doc/207762>.

@article{Zhai2005,
abstract = {We consider stabilizing a discrete-time LTI (linear time-invariant) system via state feedback where both the quantized state and control input signals are involved. The system under consideration is stabilizable and stabilizing state feedback has been designed without considering quantization, but the system's stability is not guaranteed due to the quantization effect. For this reason, we propose a hybrid quantized state feedback strategy asymptotically stabilizing the system, where the values of the quantizer parameters are updated at discrete time instants. We also extend the result to the case of static output feedback.},
author = {Zhai, Guisheng, Matsumoto, Yuuki, Chen, Xinkai, Imae, Joe, Kobayashi, Tomoaki},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {hybrid stabilization strategy; discrete-time LTI system; output feedback; state feedback; quantizer},
language = {eng},
number = {4},
pages = {509-516},
title = {Hybrid stabilization of discrete-time LTI systems with two quantized signals},
url = {http://eudml.org/doc/207762},
volume = {15},
year = {2005},
}

TY - JOUR
AU - Zhai, Guisheng
AU - Matsumoto, Yuuki
AU - Chen, Xinkai
AU - Imae, Joe
AU - Kobayashi, Tomoaki
TI - Hybrid stabilization of discrete-time LTI systems with two quantized signals
JO - International Journal of Applied Mathematics and Computer Science
PY - 2005
VL - 15
IS - 4
SP - 509
EP - 516
AB - We consider stabilizing a discrete-time LTI (linear time-invariant) system via state feedback where both the quantized state and control input signals are involved. The system under consideration is stabilizable and stabilizing state feedback has been designed without considering quantization, but the system's stability is not guaranteed due to the quantization effect. For this reason, we propose a hybrid quantized state feedback strategy asymptotically stabilizing the system, where the values of the quantizer parameters are updated at discrete time instants. We also extend the result to the case of static output feedback.
LA - eng
KW - hybrid stabilization strategy; discrete-time LTI system; output feedback; state feedback; quantizer
UR - http://eudml.org/doc/207762
ER -

References

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  1. Brockett R.W. and Liberzon D.(2000): Quantized feedback stabilization of linear systems. - IEEE Trans. Automat. Contr., Vol. 45, No. 7, pp. 1279-1289. Zbl0988.93069
  2. Bushnell L.G., Ed. (2001): Special section on networks and control. - IEEE Contr. Sys. Mag., Vol. 21, No. 1, pp. 22-99. 
  3. Delchamps D.F. (1990): Stabilizing a linear system with quantized state feedback. - IEEE Trans. Automat. Contr., Vol. 35, No. 8, pp. 916-924. Zbl0719.93067
  4. Hespanha J.P. and Morse A.S. (1999): Stability of switched systems with average dwell-time. - Proc. 38th IEEE Conf. Decision and Control, Phoenix, USA, pp. 2655-2660. 
  5. Liberzon D. (2000): Nonlinear stabilization by hybrid quantized feedback. - Proc. 3rd Int. Workshop Hybrid Systems: Computation and Control, Pittsburgh, USA, pp. 243-257. Zbl0952.93109
  6. Liberzon D. (2003): Hybrid feedback stabilization of systems with quantized signals. - Automatica, Vol. 39, No. 9, pp. 1543-1554. Zbl1030.93042
  7. Zhai G., Hu B., Yasuda K., and Michel A.N. (2001): Stability analysis of switched systems with stable and unstable subsystems: An average dwell time approach. - Int. J. Syst. Sci., Vol. 32, No. 8, pp. 1055-1061. Zbl1022.93043
  8. Zhai G., Mi Y., Imae J. and Kobayashi T. (2005): Design of H_∞ feedback control systems with quantized signals. - Prepr. 16th IFAC World Congress, Prague, Czech Republic, (on CD-ROM). 

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