Control of systems to sets and their interiors

For a closed target setSⁿ and a control system (formulated as a differential inclusion and defined nearS), the present paper considers a sufficient condition for the property that every point nearS can be steered toS 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 setS, we also consider conditions that guarantee that some trajectories enter the interior ofS.This work was supported by the Natural Sciences and Engineering Research Council of Canada and by FCAR, Québec, Canada.