×

A study on decentralized \(H_{\infty}\) feedback control systems with local quantizers. (English) Zbl 1158.93350

Summary: 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.

MSC:

93C15 Control/observation systems governed by ordinary differential equations
93C55 Discrete-time control/observation systems
93C83 Control/observation systems involving computers (process control, etc.)
93D15 Stabilization of systems by feedback
93D25 Input-output approaches in control theory
PDF BibTeX XML Cite
Full Text: EuDML Link

References:

[1] R. W. Brockett and D. Liberzon: Quantized feedback stabilization of linear systems. IEEE Trans. Automat. Control 45 (2000), 1279-1289. · Zbl 0988.93069
[2] L. G. Bushnell: Special section on networks & control. IEEE Control Systems Magazine 21 (2001), 22-99.
[3] D. F. Delchamps: Stabilizing a linear system with quantized state feedback. IEEE Trans. Automat. Control 35 (1990), 916-924. · Zbl 0719.93067
[4] H. Ishii and B. Francis: Limited Data Rate in Control Systems with Networks. Springer-Verlag, Berlin 2002. · Zbl 1001.93001
[5] T. Iwasaki, R. E. Skelton, and K. M. Grigoriadis: A Unified Algebraic Approach to Linear Control Design. Taylor & Francis, London 1998.
[6] D. Liberzon: Nonlinear stabilization by hybrid quantized feedback. Proc. 3rd Internat. Workshop on Hybrid Systems: Computation and Control, Pittsburgh 2000, pp. 243-257. · Zbl 0952.93109
[7] D. Liberzon: Hybrid feedback stabilization of systems with quantized signals. Automatica 39 (2003), 1543-1554. · Zbl 1030.93042
[8] Y. Matsumoto, G. Zhai, and Y. Mi: Stabilization of discrete-time LTI systems by hybrid quantized output feedback. Preprints of the 46th Japan Joint Automatic Control Conference, Okayama 2003, pp. 799-802.
[9] H. Zhai, Y. Matsumoto, X. Chen, and Y. Mi: Hybrid stabilization of linear time-invariant systems with two quantizers. Proc. 2004 IEEE Internat. Symposium on Intelligent Control, Taipei 2004, pp. 305-309.
[10] G. Zhai, Y. Mi, J. Imae, and T. Kobayashi: Design of \({{H}}_{\infty }\) feedback control systems with quantized signals. Preprints of the 16th IFAC World Congress, Paper code: Fr-M17-TO/1, Prague 2005.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.