Research On The Properties Of The Matrix Valued Toeplitz-bezoutian

In this paper some properties of matrix-valued Toeplitz-Bezout matrix are characterized. In Chapter 2 the formulas of Barnett factorization, triangular decomposition, the intertwining relationship with its companion matrix and other properties are discussed under the standard basis. The method is a pure algebraic approach. In Chapter 3, the T-Bezout matrix with respect to a general polynomial basis is introduced and the similar results are obtained.In final, the T-Bezout matrix can be expressed by controllability matrix and observability matrix of linear control system.