Reachability of Affine Systems on Polytopes

The paper studies reachability problem of autonomous affine systems on n-dimensional polytopes. Our goal is to obtain both the largest positive invariant setinthepolytope and the backward reachable set (the attraction domain) of eachfacet. Special attention is paid to the largest stable invariant affine subspace. After presenting several useful properties of those sets, a partition procedure is given to determine the largest positive invariant set in the polytope and all the attraction domains of facets.