Quantized Feedback Control for Sampled-Data Systems

This paper studies the problem of quantized feedback control for sampled-data systems which employ a quantizer to transmit feedback signals at a given sampling rate. The so-called static (memoryless) quantizers are considered. Given a continuous-time system, the design objective is to stabilize the system or to achieve certain performance using the coarsest quantization density. We study the possibleadvantages of over-sampling where the input/output signals of the system are sampled at a faster rate than the quantizer. Our first result is for stabilization, and it shows that the coarsest quantization density achievable using quantized state feedback can be generically achieved using output feedback with any over-sampling ratio. Our second result provides a solution to the quantized feedback H infinity problem for both with and without over-sampling.