Infinite horizon lqg control with fixed-rate quantization

In this paper, we consider infinite-horizon linear quadratic Gaussian (LQG) control systems with the constraint that the measurement signal is quantized by a fixed-rate quantizer before going into the controller. It has been shown recently that only weak separation principle holds for the LQG control system with communication channels. It has also been shown that the separation principle holds approximately for quantized LQG control in the finite-horizon setting under the assumption of high-resolution quantization. We propose an adaptive fixed-rate quantizer for feedback control design to achieve the mean-square stability and good LQG performance, where the long-term average cost is divided into two parts: the first part depends on the classical LQG cost, and the second part depends on the distortion of the quantizer.