Control Sets for Affine Systems, Spectral Properties, and Projective Spaces

Abstract

For affine control systems with bounded control range, the control sets, i.e., the maximal subsets of complete approximate controllability, are studied using spectral properties. For hyperbolic systems there is a unique control set with nonvoid interior, and it is bounded. For nonhyperbolic systems, these control sets are unbounded. In an appropriate compactification of the state space there is a unique chain control set, and the relations to the homogeneous part of the control system are worked out.