Mininal polynomial matrix and linear multivariable systems. I (Q1101045)

Part I of this work is on the theory of minimal polynomial matrix and part II [see the paper reviewed below] on the applications of this theory to linear multivariable systems. In part I, concepts of annihilating polynomial matrix and the minimal polynomial matrix of a given linear transformation in a vector group are given and the concepts of the generating system and minimal generating system of an invariant subspace for a given linear transformation are given as well. After discussing the basic properties of these concepts the relations between them and the characteristic matrix corresponding to an induced operator of a given linear transformation in any of its invariant subspaces are studied in detail. The characteristics of the minimal polynomial matrix for a given vector group and the necessary and sufficient condition for the two generating systems to have the same generating subspace is given. Using these results we can give an e actual engineering constraints and to translate those constraints into constraints on the design parameters. An example is given.