Reachable and controllable sets for two-dimensional,linear, discrete-time systems

We consider two-dimensional discrete-time linear systems with constrained controls. We propose a simple polynomial time procedure to give an exact external representation of theN-step reachable set and controllable set. The bounding hyperplanes are explicitly derived in terms of the data of the problem. By using a result in computational geometry, all the calculations are made in polynomial time in contrast to classical methods. The limit case asN is also investigated.