Some Results on an Affine Obstruction to Reach Control

This ArXiv paper is a supplement to [7] and contains proofs of preliminary claims omitted in [7] for lack of space. The paper deals with exploring a necessary condition for solvability of the Reach Control Problem (RCP) using affine feedback. The goal of the RCP is to drive the states of an affine control system to a given facet of a simplex without first exiting the simplex through other facets. In analogy to the problem of a topological obstruction to the RCP for continuous state feedback studied in [7], this paper formulates the problem of an affine obstruction and solves it in the case of two- and three-dimensional systems. An appealing geometric cone condition is identified as the new necessary condition.