Approximating Reachable Sets for n-dimensional Linear Discrete Systems

Abstract

We present a technique for approximating the reachable set from the origin for n -dimensional discrete-time linear systems subject to bounded control, where the state matrix is stable and diagonalizable. The procedure is based on decomposing the system into one- and two-dimensional subsystems for which the reachable set of each of the subsystems can be over-estimated by a polygon. These polygons are then used to create an n -dimensional polyhedron which contains the reachable set of the original system