Approximation of RCI set contained within a 2-norm ball or an ellipsoid

Abstract

In this paper, we establish both a necessary and sufficient condition, as well as a sufficient condition, for non-empty sets to be contained within a 2-norm ball or an origin-centered ellipsoid. When the constraint sets of a discrete-time linear time-invariant system subjected to bounded disturbances are either 2-norm balls or ellipsoids, we formulate a series of linear programming problems using the proposed conditions to compute the robust control invariant (RCI) sets under such constraint sets. Finally, we design an algorithm to compute the minimal-volume outer approximation of the minimal robust control invariant (mRCI) set within a fixed tolerance. Numerical examples validate the effectiveness of the proposed results.