Optimal input sets for steering quantized systems

Limited capacity of communication channels has strongly pushed the analysis of control systems subject to a quantized input set. Quantized control system of type x + = x + u , where the u takes values in a set of 2 m + 1 integer numbers, symmetric with respect to 0 arise in some fundamental situations, e.g., flat, nilpotent, and linear systems with quantized feedback. In this paper we consider this special type of systems and analyze the reachable set after K steps. We find explicit expressions, for each K and for each m , of m input values such that the reachable set after K steps is as large as possible.