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

Given an affine system on a simplex, the problem of reaching a particular facet of the simplex, using affine state feedback is studied. Necessary and sufficient conditions for the existence of a solution are derived in terms of linear inequalities on the input vectors at the vertices of the simplex. If these conditions are met, a constructive procedure yields an affine feedback control law, that solves this reachability problem