LQG control with fixed-rate uniform quantization for SISO systems

This paper considers the quantized infinite-horizon LQG control system, of which the measurement signal is quantized by a fixed-rate quantizer before going into the controller. It turns out that only weak separation principle holds for the LQG control system with communication channels. We study the problem of quantized LQG for a single-input-single-output (SISO) system. An adaptive fixed-rate quantizer is designed to achieve the mean-square stability and the optimal distortion performance. For a quantizer with a fixed bit rate of R (per sample), we show that the quantization distortion order is R2^-2R for a large R. Simulation examples are given to demonstrate the effectiveness of the proposed methods.