Quantized feedback control for linear uncertain systems

This paper studies robust control problems under the setting of quantized feedback. We consider both the static and dynamic logarithmic quantizers. In the static quantization case, the quantizer has an infinite number of levels, and the design problem is to find the minimal quantization density required to achieve a given control objective. In the dynamic quantization case, the problem is to minimize the number of quantization levels to achieve a given control objective. We present a number of results for different controller-quantizer configurations. These results are developed using the so-called sector bound approach for quantized feedback control, which was initiated by the authors previously for systems without uncertainties. Copyright © 2009 John Wiley & Sons, Ltd.

[1]  Daniel Liberzon,et al.  Quantized feedback stabilization of linear systems , 2000, IEEE Trans. Autom. Control..

[2]  Nicola Elia,et al.  Stabilization of linear systems with limited information , 2001, IEEE Trans. Autom. Control..

[3]  T. Fischer,et al.  Optimal quantized control , 1982 .

[4]  Chung-Yao Kao,et al.  Stabilization of linear systems with limited information multiple input case , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[5]  Wing Shing Wong,et al.  Systems with finite communication bandwidth constraints. II. Stabilization with limited information feedback , 1999, IEEE Trans. Autom. Control..

[6]  B. Widrow.  Statistical analysis of amplitude-quantized sampled-data systems , 1961, Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry.

[7]  Lihua Xie,et al.  H∞ analysis and synthesis of discrete-time systems with time-varying uncertainty , 1993, IEEE Trans. Autom. Control..

[8]  Emilio Frazzoli,et al.  Quantized Stabilization of Two-Input Linear Systems: A Lower Bound on the Minimal Quantization Density , 2002, HSCC.

[9]  Lihua Xie,et al.  The sector bound approach to quantized feedback control , 2005, IEEE Transactions on Automatic Control.

[10]  R. Evans,et al.  Stabilization with data-rate-limited feedback: tightest attainable bounds , 2000 .

[11]  R. Larson,et al.  Optimum quantization in dynamic systems , 1967, IEEE Transactions on Automatic Control.

[12]  Lihua Xie,et al.  Output feedback H∞ control of systems with parameter uncertainty , 1996 .

[13]  D. Delchamps.  Stabilizing a linear system with quantized state feedback , 1990 .

[14]  R. Brockett,et al.  Systems with finite communication bandwidth constraints. I. State estimation problems , 1997, IEEE Trans. Autom. Control..

[15]  J. Farrell,et al.  Quantizer effects on steady-state error specifications of digital feedback control systems , 1989 .

[16]  N. Elia.  Design of hybrid systems with guaranteed performance , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).