ϵ-approximation of differential inclusions

For a Lipschitz differential inclusion x˙∈f(x), we give a method to compute an arbitrarily close approximation of Reach_f(X₀,t)-the set of states reached after time t starting from an initial set X₀. We also define a finite sample graph, A^ε, of the differential inclusion x˙∈f(x). Every trajectory φ of the differential inclusion x˙∈f(x) is also a “trajectory” in A^e. And every “trajectory” η of A^e has the property that dist(η˙(t),f(η(t)))⩽ε. Using this, we can compute the ε-invariant sets of the differential inclusion-the sets that remain invariant under small perturbations in f