NON-OVERLAPPING CONTROL SYSTEMS ON AFF(R)

Let G be a Lie group with Lie algebra L(G) and let $\Omega$ be a nonempty subset of L(G). If $\Omega$ is interpreted as the set of controls, then the set of elements attainable from the identity for the system $\Omega$ is a subsemigroup of G. A system $\Omega$ is called a non-overlapping control system if any element attainable for $\Omega$ is only attainable at one time.