Design of reach controllers on simplices

We examine currently available methods to design reach controllers on simplices under the assumption of a preferred triangulation of the state space. Using an example-driven approach, we show that existing methods completely resolve how reach controllers can be designed under this triangulation. The paper begins by examining the simplest cases using affine feedbacks. Then using the reach control indices we look at cases when the design calls for either discontinuous piecewise affine feedback or time-varying affine feedback.