ε-approximation of differential inclusions

For a Lipschitz differential inclusion x/spl dot//spl isin/f(x), we give a method to compute an arbitrarily close approximation of Reach/sub f/(X/sub 0/,t)-the set of states reached after time t starting from an initial set X/sub 0/. We also define a finite sample graph, A/sup /spl epsiv//, of the differential inclusion x/spl dot//spl isin/f(x). Every trajectory /spl phi/ of the differential inclusion x/spl dot//spl isin/f(x) is also a "trajectory" in A/sup e/. And every "trajectory" /spl eta/ of A/sup e/ has the property that dist(/spl eta//spl dot/(t),f(/spl eta/(t)))/spl les//spl epsiv/. Using this, we can compute the /spl epsiv/-invariant sets of the differential inclusion-the sets that remain invariant under small perturbations in f.