Reach control on simplices by piecewise affine feedback

We study the reach control problem for affine systems on simplices, and the focus is on cases when it is known that the problem is not solvable by continuous state feedback. Using the reach control indices for affine systems on simplices, we propose a subdivision algorithm and associated piecewise affine feedback. The main result is that if the reach control problem is solvable by open-loop controls, then it is solvable by piecewise affine feedback.