REACHABILITY PROPERTIES OF CONSTRAINED LINEAR-SYSTEMS

This paper presents reachability results for a linear control system and arbitrary terminal points p in R(n) with controls constrained within a compact set U containing the origin. The well-known results for p = 0 are then a special case of our results. Geometric properties of the reachable set are presented and include: general containment properties which describe conditions that guarantee the inclusion of a reachable set in another reachable set; classification of the set of all points p that ensure the equivalence of two (different) reachable sets and the properties of this set. The topological properties of the reachable set to a point p depends on the control set U, the final point p, and the location of the spectrum of the system in the complex plane. We characterize the geometric properties of the reachable set when the spectrum lies in the closed right-half plane, the open left-half plane, or a combination of both.