Feedback stabilization of MIMO nD linear systems

The open problem of the existence of double coprime factorizations (DCFs) for multi-input/multi-output (MIMO) multidimensional (nD) linear systems is considered in the paper. It is shown that DCFs exist for a class of MIMO nD linear systems. A simple and efficient method is proposed for the construction of DCFs. The main result of the paper is to show how to construct a coprime (over the ring of stable rational functions) matrix fraction description of a given MIMO nD system with a stable reduced minor. A parameterization of all stabilizing compensators is given for a MIMO nD system in this class. An example is illustrated.