Any Domain of Attraction for a Linear Constrained System is a Tracking Domain of Attraction

We face the problem of determining a tracking domain of attraction, say the set of initial states starting from which it is possible to track reference signals in given class, for discrete-time systems with control and state constraints. We show that the tracking domain of attraction is exactly equal to the domain of attraction, say the set of states which can be brought to the origin by a proper feedback law. For constant reference signals we establish a connection between the convergence speed of the stabilization problem and tracking convergence which turns out to be independent of the reference signal. We also show that the tracking controller can be inferred from the stabilizing (possibly nonlinear) controller associated with the domain of attraction. We refer the reader to the full version [17], where the continuous-time case, proofs and extensions are presented.