Abstract: part (Ⅰ) of this work is on the theory of minimal polynomial matrix and Part (Ⅱ) is on the applications of this theory to linear multivariable systems.In I of this part, using the theory in Part (Ⅰ), some results about input part of a linear multivariable system are discussed in detail and in II, using duality properties, the concepts about row n.p.m.and row generating system, etc. are given, and some results about output part of linear multivariable system are discussed, too. In III, we discuss the approach which can give the polynomial model with less dimension from the state-space modeland in IV we discuss tha inverse of the problem to give the state-space model from the polynomial model. Some interesting examples are given to explain the theory and the approach.

Key words: infinite field, infinite analytical element, Hamiltonian system, method of eigenfunction expansion, FEM