Dynamic Quantized Feedback Control Design for Uncertain Linear Systems

Quantized feedback control design has attracted a lot of attention because of the increased interest in considering feedback control over digital communication networks. A significant amount of work has been done on the use of static (or memoryless) quantizers. These quantizers are relatively simple to study and to implement. However, the use of dynamic quantizers can significantly compress the amount of quantized feedback information. Research on dynamic quantizers for feedback control is quite immature yet. Few design methods of this kind are practical and easily implementable. In this paper, we study a simple dynamic scaling method for quantizer design and the application of it to control of uncertain linear systems. We show that this sort of simple dynamic quantizers only require a moderate information rate for robust stabilization of linear systems. Results are illustrated via examples. We show that the typical information rate is only a few bits per sample.