Feedback stabilization of MIMO 3-D linear systems

The authors solve the open problem of the existence of double coprime factorizations for a large class of multi-input/multi-output (MIMO) three-dimensional (3-D) linear systems. It is proven that if all the unstable zeros of the contents associated with left and right matrix fraction descriptions of a given feedback stabilizable causal MIMO 3-D plant are simple, then the plant has a double coprime factorization. The authors then give a parameterization of all stabilizing compensators for a MIMO 3-D system in this class. The key result developed in the paper is a novel and constructive technique of “replacing” an unstable polynomial with a stable polynomial step by step. An illustrative example is also provided