An optimal quantized feedback strategy for scalar linear systems

We give an optimal (memoryless) quantized feedback strategy for stabilization of scalar linear systems, in the case of integral eigenvalue. As we do not require the quantization subsets to be intervals, this strategy has better performances than allowed by the lower bounds recently proved by Fagnani and Zampieri. We also describe a general setting, in which we prove a necessary and sufficient condition for the existence of a memoryless quantized feedback to achieve stability, and provide an analysis of Maxwell's demon in this context.