An Approximation of the State Reachable Set with Guaranteed Accuracy for Discrete-time Systems

Abstract

This paper considers an approximation problem of the state reachable set for linear discrete-time systems with unknown but bounded disturbance inputs. A simple recursive procedure provides a sequence of enlarging convex polyhedral sets which successively approximate the state reachable set. The notion of positive invariance is utilized to derive the stopping criterion for the proposed recursion. The procedure makes possible that an approximation of the state reachable set within the required accuracy.