Approximation of RCI Set Under p-Norm Ball Constraints for Linear Discrete-Time Systems

This paper investigates the approximation of robust control invariant (RCI) sets for linear discrete-time systems subject to p-norm ball constraints (p≥1). Unlike classical results focusing on specific cases like polytope or ellipsoid constraints, we propose a unified framework for arbitrary p-norm ball constraints. Sufficient conditions for a non-empty set to be contained within a p-norm ball are established, revealing the geometric insight that the set is essentially contained within the inscribed 2-norm ball. Utilizing these results, the approximation problem of the RCI set is formulated as a standard linear programming problem that requires verifying constraints at only n standard basis vectors, significantly reducing computational complexity. Specific optimization models are derived, and numerical experiments demonstrate the effectiveness and competitive accuracy of the proposed method.