Linear quadratic Gaussian control with quantized feedback

This paper studies a generalized linear quadratic Gaussian (LQG) control problem subject to the constraint that the feedback signal is quantized with a fixed bit rate. We show that state feedback control, state estimation and quantization can not be fully separated in general. Only a weak separation principle holds which converts the quantized LQG control problem into a quantized state estimation problem. We show that under high resolution quantization and the assumption that the output dimension does not exceed the input dimension, full separation of state feedback control, state estimation and quantization can be achieved.