Pointwise completeness and pointwise degeneracy of 2D standard and positive Fornasini-Marchesini models with state-feedbacks

Necessary and sufficient conditions are established for the pointwise completeness of 2D standard and positive Fornasini-Marchesini models with state-feedbacks. Similar relations are obtained for the pointwise degeneracy of the 2D models with state-feedbacks. It is shown that if the positive 2D model is pointwise complete then there exists a gain matrix of the state-feedback such that the closed-loop system is pointwise degenerated if both matrices B1 and B2 of the 2D Fornasini-Marchesini model are nonzero. The considerations are illustrated by numerical examples.