Invariant approximations of robustly positively invariant sets for constrained linear discrete-time systems subject to bounded disturbances

This paper provides results on invariant approximations of robustly positively invariant sets for a discrete-time, linear, time-invariant system subject to state constraints. Two important sets, the minimal and the maximal robustly positively invariant sets and their approximations are investigated. Novel procedures for the computation of invariant approximations to these sets are presented. It is assumed that the disturbance is bounded, persistent and acts additively on the state and that the constraints on the state and disturbance are polyhedral.