Quantized Control Systems and Discrete Nonholonomy

In this paper we study control systems whose input sets are quantized, and in particular finite or countable but nowhere dense. We specifically focus on problems relating to the structure of the reachable set of such systems, which may turn out to be either dense or discrete. We report results on the rechable set of linear quantized systems, and on a particular but interesting class of nonlinear systems, forming the discrete counterpart of driftless nonholonomic continuous systems. Implications and open problems in the analysis and synthesis of quantized control systems are addressed.