1. A method for automatically determining reachable states of a hybrid system utilizing template polyhedra, constructed in part using linear template expressions, comprising: generating a set of template polyhedra expressions from a system description; employing policy iteration to produce an over-approximation of states reachable by the hybrid system from the expressions in the form of a relaxed invariant; and constructing a flowpipe of template polyhedra based on the relaxed invariant obtained from policy iteration to refine the over-approximation of reachable states and thereby determine the reachable states of the hybrid system.