Robust stabilization of linear uncertain systems via quantized feedback

This paper studies the problem of robust stabilization for linear uncertain systems via logarithmic quantized feedback. Our work is based on a new method for the analysis of quantized feedback. More specifically, we characterize the quantization error using a simple sector bound. It is shown in our previous work that this method yields the same result on the coarsest quantization density as in the work of Elia and Mitter, when the system does not involve uncertainties. The advantage of this new method is that it is applicable to multi-input-multi-output systems and to performance control problems. In this paper, we apply this method to robust stabilization of linear uncertain systems. We give conditions under which there exists a quadratic stabilizing controller for a given quantization density. Both state feedback and output feedback are considered. For output feedback, we consider two cases: 1) quantization occurs at the control input; and 2) quantization occurs at the measured output.