Structural stabilization of linear 2D discrete systems using equivalence transformations

We consider stability and stabilization issues for linear two-dimensional (2D) discrete systems. We give a general definition of structural stability for all linear 2D discrete systems which coincides with the existing definitions in the particular cases of the classical Roesser and Fornasini–Marchesini discrete models. We study the preservation of the structural stability by equivalence transformations in the sense of the algebraic analysis approach to linear systems theory. This allows us to use recent works both on the stabilization of linear 2D Roesser models and on the equivalence of linear multidimensional systems in order to develop a stabilization method for linear 2D discrete Fornasini–Marchesini models.

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