Stably-freeness and multidimensional systems with structural stability

We are concerned with the multidimensional systems based on the algebraic approach. In the case of noncommensurate delays, there are some stabilizable plants that do not have coprime factorizations. We consider the stably-freeness and Hermite as intermediate notions of coprime factorizability. We give that when noncommensurate delays are considered in the sense that we cannot use the unit delay, even if the stably-freeness does not hold, the set of stable causal transfer functions is Hermite in general. Further we present the parameterization of the stabilizing controller that can be applied even if there is not one of right-/left-coprime factorization.