The pole assignment problems of linear systems by decentralized static output feedback are considered in this paper. A compactification of decentralized static feedback space, product Grassmannians, is introduced in this paper. Its degree under Plucker-Segre embedding is computed. Sufficient conditions for arbitrary and almost arbitrary pole assignability are given. It is also proved that the generic m × p system of McMillan degree n has arbitrary pole assignability by r-channel decentralized static output with mi inputs and pi outputs on the ith channel if ∑i=1r mipi ≥ n when the degree of the product Grassmannians is odd, or if ∑i=1r mipi > n and the local channels have either the same numbers of inputs or the same numbers of outputs when the degree of the product Grassmannians is even.