Quantization of linear systems

In this paper, we show that the coarsest quantizer that quadratically stabilizes a single input linear discrete time invariant system is logarithmic, and can be computed by solving a special linear quadratic regulation problem. We provide a closed form for the optimal logarithmic base exclusively in terms of the unstable eigenvalues of the system. We show how to design quantized state-feedback in general, and quantized state estimators in the case where all the eigenvalues of the system are unstable. This leads to the design of output feedback controllers with quantized measurements and controls