On (A, B)-invariance of polyhedral domains for discrete-time systems

The problem of confining the trajectory of a discrete-time linear system in a given polyhedral set is addressed using the positive invariance approach. The property of (A, B)-invariance of polyhedral domains is introduced. It is then geometrically and analytically characterized. In particular, this property is verified by the maximal admissible set included in a given polyhedral domain. An important class of (A, B)-invariant polyhedral domains admitting a linear state feedback invariant control law is exhibited. The results are extended to systems subject to additive disturbances.