A lattice approach to analysis and synthesis problems

Within a lattice approach, the purpose of this paper is to give general necessary and sufficient conditions for internal stabilizability and for the existence of (weakly) left-/right-/doubly coprime factorizations of multi input multi output linear systems. These results extend the ones recently obtained in [24] for single input single output systems. In particular, combining these results with the one obtained in [3,13], we prove that every internally stabilizable multidimensional system admits doubly coprime factorizations, solving Lin’s conjecture [17,18].