The matrix partial realization problem: an algebraic approach

This paper introduces a new approach to the multivariable partial realization problem. It formulates the problem in algebraic terminology, which sheds new light on the nature of the problem and our existing knowledge of it. The structure of the state space is analysed in terms of polynomial models. The main idea is analysis of the algebraic structure of the kernels of truncated Hankel maps. The elements of such kernels are directly related to the partial realization problem, in the sense that the columns of the denominator matrix of a partial realization are elements of such kernels. The numerator matrix is determined by an appropriate denominator matrix