Control of Systems to Sets and Their Interiors

For a closed target set S ⊂ R and a control system (formulated as a differential inclusion and defined near S), the present paper considers a sufficient condition for the property that every point near S can be steered to S in finite time by some trajectory of the system. Estimates are obtained revealing how fast some such trajectory is nearing the target. A strong form of this condition is shown to imply that every trajectory of the system hits the target. With a further assumption on the target set S, we also consider conditions that guarantee that some trajectories enter the interior of S.