In this work the concept of self-bounded (A,B)-invariant sets is analyzed, as well as its implication in constrained controllability of discrete-time systems subject to state constraints. Self-bounded (A,B)-invariant sets are defined and characterized. It is shown that the class of self-bounded sets contained in a given region has an infimum, that is, a self-bounded set which is contained in any set of this class. The infimal set is characterized and a numerical method is presented for its computation in the polyhedral case. These results are then used to analyze the problem of constant reference tracking for state constrained systems. The results are illustrated by a numerical example.
Linear systems; invariance; geometric approaches; feedback control
