A Constructive Solution to Interconnection and Decomposition Problems with Multidimensional Behaviors

An algorithm for SDV representation of 2D behaviors

“…Note that such a L-polynomial matrix exists, see for instance [8]. Thus, we shall show that L is a least common left factor of R 1 and R 2 .…”

“…Hence P is zero right prime. Moreover, recalling that det M is cw-unital, from (8), det(∆) is cw-unital. Consequently, also det(∆) is cw-unital.…”

On the regular implementability of nD systems

“…In the remarkable paper [15,Theorem 3.2] this condition was shown to be equivalent to the solvability of a linear polynomial matrix equation (see also [3]). …”

“…In the behavioral approach to control this problem has been formalized as the problem of characterizing all behaviors that are implementable with respect to the given plant behavior. Originally the problem was mainly studied for 1D systems, see for example [14,2,1,7], but also generalizations to more general classes of system behaviors, including nD systems, have been investigated, see [12,10,4,15].…”

“…A characterization of all regularly implementable behaviors, in the 1D context, was established for the first time in [2], see also [1,13]. At approximately the same time, in the nD context, in [10] and also in [15] necessary and sufficient conditions were given for regular implementability by full interconnection, the special case that the c variable and the w variable coincide. More recently, in [10] regular implementability by partial interconnection was investigated also in the nD context.…”