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.

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CWI
CWI. Probability, Networks and Algorithms [PNA]
Stochastics

Habets, L.C.G.J.M, & van Schuppen, J.H. (2000). A control problem for affine dynamical systems on a full-dimensional simplex. CWI. Probability, Networks and Algorithms [PNA]. CWI.