Resolving Control to Facet Problems for Affine Hypersurface Systems on Simplices
Zhiyun Lin, Mireille E. Broucke · 2006
We study control to facet problems for affine hypersurface systems on simplices. An easily verifiable necessary and sufficient condition is derived that allows one to determine whether there is a linear affine feedback driving all trajectories of the closed-loop system out of the simplex through a desired facet. In cases where the condition is violated, methods are developed to establish the largest subset of the simplex such that there is still a feedback control (not necessarily linear) which can steer all trajectories starting from this set to the desired facet without crossing other facets. The results are demonstrated on a circuit with a piecewise linear resistor