Characterization of backward reachable set and positive invariant set in polytopes

The paper studies reachability problems of autonomous affine systems in polytopes. Our goal is to find in a given polytope both the largest positive invariant set and backward reachable sets (or attraction domains) of facets. Special attention is paid to the stable invariant affine subspace. After presenting several useful properties of these sets, a partition procedure is given so that the polytope is divided into a positive invariant set and several backward reachable sets.