Minimal realizations and transmission zeros of transfer-function matrices

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1976

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Abstract

In the analysis and synthesis of control systems and circuits, the minimal realizations of transfer-function matrices are often desired for the reasons of economy and sensitivity. A new and efficient method which uses the matrix continued fraction is derived in this research for obtaining the minimal realizations of transfer-function matrices. A necessary and sufficient condition is also derived to determine the existence of the matrix continued fraction. The transmission zeros which block the input signals to the outputs of multivariable systems play important roles in the analysis and synthesis of control systems and circuits. The occurrence of these zeros can be thought of as a consequence of the structural natural of the multivariable systems which can be expressed by the minimal dynamic equations. A frequency domain approach which uses the matrix Routh algorithm and the reverse process of the matrix Routh algorithm is presented in this research to construct relatively prime polynomial matrices and to determine the transmission zeros of multivariable systems with various inputs and outputs. A method of undetermined coefficients is also derived to find the determinant of a polynomial matrix.

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