Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 13 (2006), No. 2, 253--267Copyright Heldermann Verlag 2006 Perimeter Estimates for Reachable Sets of Control Systems Piermarco Cannarsa Dip. di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy cannarsa@axp.mat.uniroma2.it Pierre Cardaliaguet UFR Sciences Techniques, Lab. de Mathématiques, Université de Bretagne Occ., 6 Av. Victor Le Gorgeu, 29283 Brest, France Pierre.Cardaliaguet@univ-brest.fr [Abstract-pdf] The reachable set in time $T>0$, ${\cal R}(T)$, is here investigated for the symmetric control system $\dot x (t)=f(x(t))u(t)$, $u(t)\in\overline{B}$. It turns out that, for $f(x)$ smooth and nondegenerate, ${\cal R}(T)$ has finite perimeter, and a sharp estimate for the time-dependence of the perimeter and volume of such a set can be obtained. Keywords: Control theory, attainable sets, interior ball condition, sets of finite perimeter. [ Fulltext-pdf  (436  KB)] for subscribers only.