Some complements about reachability and pole placement for implicit systems

One of the most important features of the reachability of a state space representation is the complete assignability of the closed loop spectrum by means of a state feedback. This equivalence is no longer the case when dealing with implicit representations. For the reachable implicit description case, a geometric condition has to be added in order to guarantee such a pole assignment ability. In this paper, we give geometric conditions, which enable us to assign the closed loop spectrum of: (i) a reachable implicit description, and (ii) a reachable and observable implicit description with output equation.