Positively invariant polyhedral sets of discrete-time linear systems

Abstract

The problem of the existence of positively invariant polyhedral sets for linear discrete-time dynamical systems is studied. In the first part of the paper, necessary and sufficient conditions for a given polyhedral set to be a positively invariant set of a linear system are obtained. Then, the spectral properties of systems possessing this kind of invariant set are established. Finally the class of systems possessing positively invariant polyhedral cones is studied.