Self-bounded (A,B)-invariant polyhedra of discrete-time systems

This work extends the concept of self-bounded (A,B)-invariant subspaces to convex polyhedral sets. Self-bounded (A,B)-invariant polyhedra are defined and characterized. Necessary and sufficient conditions under which a given polyhedron is self-bounded are established in the form of linear matrix relations. It is then 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 proposed for its computation in the polyhedral case. It is also shown how these results can be extended to systems subject to control constraints and bounded additive disturbances. A numerical illustrative example is finally presented