ϵ-feasible approximation of the state reachable set for discrete-time systems

This paper considers an approximation problem of the state reachable set for linear discrete-time systems with unknown but bounded exogenous inputs. A simple recursive procedure provides a sequence of enlarging convex polyhedral sets which successively approximates the state reachable set. The main contribution of this paper is to clarify a stopping criterion for the recursive procedure. The notion of positive invariance is utilized to derive the stopping criterion. The procedure makes it possible, as it is contrast to those of other existing methods, to estimate the state reachable set within a required accuracy.