Control of multi-affine systems on rectangles with applications to hybrid biomolecular networks

Given a multi-affine system on an N-dimensional rectangle, the problem of reaching a particular facet, using multiaffine state feedback is studied. Necessary conditions 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 rectangle, and a method for constructing a multi-affine state feedback solution is presented. The technique is applied to the control of hybrid models of bioregulatory networks.