Reachability of Affine Systems on Polytopes
多面体上彷射系统可达性问题研究

The paper studies reachability problem of autonomous affine systems on n-dimensional polytopes. Our goal is to obtain both the largest positive invariant set in the polytope and the backward reachable set (the attraction domain) of each facet. 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.