Finite Rank and Decomposition of Infinite Generalized Block Hankel Matrix

Infinite generalized block Hankel matrix is associated with controllability matrix and transfer function matrix of multi-input and multi-output linear system, the finite rank and decomposition of infinite generalized block Hankel matrix are discussed, it is obtained the necessary and sufficient condition of that infinite generalized block Hankel matrix has finite rank and that any infinite. generalized block Hankel matrix could be decomposed a product of two matrices, which are the infinite block observability matrix and the infinite block controllability matrix of the minimal realization system in its corresponding strictly proper rational fraction function matrix. In addition, the invertibility of finite block Hankel matrix is also discussed. A new method to study this class of matrices and their relative matrices is presented.