AbstractThe linear‐quadratic‐Gaussian problem of quantized control subject to quantized measurements is considered with the measurement and control quantizers formulated as data compression systems. The optimum closed‐loop control is shown to be separable in control law, control quantizer and estimation. However, estimation and measurement quantization are non‐separable. The optimum measurement quantizer is of a differential structure but requires optimum state estimation at both encoder and decoder. A fixed total number of quantization levels should be equally allocated to the measurement and control quantizers, and the quantizer design depends on both the known control law and the solution to the matrix Riccati equation. A suboptimum control structure is developed, and the effect of quantization error on estimation error is shown to be