Invariant Approximations of the Maximal Invariant Set or “Encircling the Square”

Abstract

This paper offers a method for the computation of invariant approximations of the maximal invariant set for constrained linear discrete time systems subject to bounded, additive, disturbances. The main advantage of the method is that it generates invariant sets at any step of the underlying set iteration. Conditions under which the sequence of generated invariant sets is monotonically non–decreasing and converges to the maximal invariant set are provided. Explicit formulae for the estimates of the Hausdorff distance between the underlying iterates and the maximal invariant set are derived.