Structural insights in constructive procedures for multidimensional realization and LFR uncertainty modeling

In this work, we review some new developments accomplished by the author and co-workers very recently for multidimensional (nD) realization and LFR uncertainty modeling. In particular, we shall show some substantial structural insights to this difficult problem that have not been clarified previously and new constructive procedures that can generate a low-order, possibly minimal Roesser model realization for a rational or polynomial nD transfer matrix with numerical or/and symbolic coefficients. It will also be demonstrated by non-trivial examples that the proposed procedures are much more effective than the existing ones.