Study of Asymptotic Stability for 2D Fornasini-Marchesini linear models

In this paper, we study directly the asymptotic stability of a particular class of linear 2D discrete Fornasini-Marchesini model. The study is challenging mathematically because it is based on the explicit form of the solutions, therefore we limit the study to the case where model matrices are commutative. We propose a new conjecture to directly test asymptotic stability based on the eigenvalues of the model matrices and we support our conjecture with numerical evidence.