Optimal input sets for time minimality in quantized control systems

Limited capacity of communication channels has brought to the attention of many researchers the analysis of control systems subject to a quantized input set. In some fundamental cases such systems can be reduced to quantized control system of type x+ = x + u, where the u takes values in a set of 2m + 1 integer numbers, symmetric with respect to 0. In this paper we consider these types of systems and analyse the reachable set after K steps. Our aim is to find a set of m input values such that the reachable set after K steps contains an interval of integers [−N, . . . , N ] with N as large as possible. For m = 2, 3 and 4, we completely solve the problem and characterize the metric associated to this quantized control system.