The properties of the decentralized pole placement map under constant output feedback are investigated and they are linked to known invariants of the decentralized pole assignment problem. A new expression of the differential of this map allows the derivation of relationships between the decentralized Plucker matrix invariant and the Markov parameters and leads to the definition of the Decentralized Markov Parameters (DMP). The matrix associated with the DMPs provides a new simple test for selection of decentralization schemes using as criteria the avoidance of formation of fixed modes and the preconditioning of the decentralized problem to be linearly assignable which excludes also almost fixed modes and it is a necessary condition for solution of the decentralized control problem. The natural link of this test to the Markov parameters and state space parameters of the models provides the means for affecting the shaping of properties of Plucker matrices by design, redesign of the input, and output structure of the system model. The results which are originally presented for the decentralized constant output feedback are subsequently extended to the case of decentralized PI feedback.