Nested strategies for the quantized feedback stabilization

A state feedback with finitely many quantization levels yields only the so called practical stabilization, namely the convergence of any initial state belonging to a bigger bounded region into another smaller target region of the state space. The ratio between the measure of the starting region and the target region is called contraction of the closed loop system. In the performance analysis of a stabilization strategy based on a quantized state feedback, two parameters play a central role: the number of quantization levels used by the feedback and the convergence time of the closed loop system. In this paper we propose a general strategy yielding a family of stabilizing quantized feedbacks from a base one and we analyze the performance of three different applications of this method.