Coprime factorizations of multivariate rational matrices

Coprime factorization is a well-known issue in one-dimensional systems theo ry, having many applications in realization theory, balancing, controller s ynthesis, etc. Generalization to systems in more than one independent varia ble is a delicate matter: First, several nonequivalent coprimeness notions for multivariate polynomial matrices have been discussed in the literature: zero, minor, and factor coprimeness. Here we adopt a generalized version o f factor primeness that appears to be most suitable for multidimensional sy stems: a matrix is prime iff it is a minimal annihilator. After reformulati ng the sheer concept of a factorization, it is shown that every rational ma trix possesses left and right coprime factorizations that can be found by m eans of computer algebraic methods. Several properties of coprime factoriza tions are given in terms of certain determinantal ideals.