Geometric properties of constrained linear systems

This paper presents results on reachability and constrained controllability properties for a class of linear control system. The geometric characterizations given are important because nonlinear systems, especially bilinear systems, do not have a priori preferred origins to be referred to and one natural way to find solutions of these systems is to linearize the model, but not necessarily at the origin. Reachable set properties are also important for derivation of minimum-time control strategies and constrained controllability properties of dynamic systems. Results presented include properties of the reachable set such as openness, convexity and inclusion in another reachable set. It is shown that its boundedness is directly related to the region where the spectrum of A lies in the complex plane. Controllability is defined and proven to be equivalent to an inclusion property of reachable sets