Convergence of an algorithm to find maximal state constraint sets for discrete-time linear dynamical systems with bounded controls and states

In [1] an algorithm was presented to find an approximant to the maximal state constraint set for a linear discrete time dynamical system with polyhedral state and input bounds. Here it is shown that the algorithm will yield an approximant arbitrarily close to the maximal state constraint set and the number of iterations is given as a function of the prescribed precision of the approximant.