A new block-Routh array with block-Routh algorithm is developed to extract the greatest common matrix polynomial of two matrix polynomials that are not coprime, and to construct a block-transformation matrix that transforms a block-state equation from a block-companion form to a block-tridiagonal form. The newly developed block-state equation in the block-tridiagonal form is a minimal realisation of a matrix-transfer function. Also, the block-state equation is used to synthesise a driving-point impedance matrix. A stability criterion is then derived to test the stability of a class of matrix transfer functions.

Erratum: Analysis and synthesis of matrix transfer functions using the new block-state equations in block-tridiagonal forms

A design method, which decouples an interactive system by using a compensator obtained from the plant inverse matrix, which is often called the direct-decoupling method is modified in this paper. The modified direct-decoupling method uses the adjoint matrix instead of the inverse of the plant matrix to construct the compensator. The method uses a frequency-domain model-reduction method to simplify the degree of the given plant transfer function matrix and the obtained compensator. For an open-loop stable multivariable system, the proposed method gives a simple, practical, and realizable controller without using an unstable pole-zero cancellation approach.

A Modified Direct-Decoupling Method for Multivariable Control System Designs

This paper presents two generalized matrix continued-fraction descriptions in the second Cauer form from a transfer function matrix and/or matrix fraction descriptions which may contain non-square and/or non-regular polynomial matrices. It also presents two model reduction techniques for model simplification of high-degree non-square transfer function matrices and matrix fraction descriptions. The expansion algorithms as well as the inversion algorithms for the generalized matrix continued-fraction descriptions are derived. Two model reduction techniques, which are the matrix continued-fraction expansion method and the mixed method of the matrix continued-fraction expansion method and the equivalent-dominant pole method, are developed for model simplification of multivariable control systems.

The generalized matrix continued-fraction descriptions and their application to model simplification†

A state-space technique is presented for minimal realization of an impedance matrix or a voltage transfer function matrix without using integrators or the combination of integrators and multiwinding transformers. The Cauer II type passive RC ladder multiport and state-space concepts are employed for the realization. A new similarity transformation matrix is derived to transform a state-space equation in a RC-type Cauer second form into a state-space equation in a block companion form.

Realization of Matrix Transfer Functions via a State-Space Approach

http://ieeexplore.ieee.org/iel5/31/23520/01085069.pdf

The authors wish to express their gratitude to the reviewers for their valuable comments and suggestions.

A purely algebraic method which uses the matrix Routh algorithm and its reverse process of the algorithm is presented to decompose a matrix transfer function into a pair of right co-prime polynomial matrices or left co-primo polynomial matrices. The poles and transmission zeros of the matrix transfer function are determined from a pair of relatively prime polynomial matrices. Also, the common divisor of two matrix polynomials can be obtained by using the matrix Routh algorithm and the matrix Routh array.

L. S. Shieh

Papers

An algebraic method to determine the common divisor, poles and transmission zeros of matrix transfer functions