This paper analyzes the relation of viability kernels and control
sets of control affine systems. A viability kernel describes
the largest closed viability domain contained in some closed subset
Q of the state space. On the
other hand, control sets are maximal regions of the state space
where approximate controllability holds. It turns out that
the viability kernel of Q can be represented by the union of
domains of attraction of chain control sets, defined relative
to the given set Q.
In particular, with this
result control sets and their domains of attraction
can be computed using techniques for the
computation of attractors and viability kernels.