A control problem for affine dynamical systems on a full-dimensional polytope

Given an a ne system on a full-dimensional polytope, the problem of reaching a particular facet of the polytope, using continuous piecewise-a ne state feedback is studied. Necessary conditions and su cient conditions for the existence of a solution are derived in terms of linear inequalities on the input vectors at the vertices of the polytope. Special attention is paid to a ne systems on full-dimensional simplices. In this case, the necessary and su cient conditions are equivalent and a constructive procedure yields an a ne feedback control law, that solves the reachability problem under consideration. ? 2003 Elsevier Ltd. All rights reserved.