The use of matrix signal-flow graph in state-space formulation of feedback theory

Presents a unified summary on the formulation of the general feedback theory in terms of the coefficient matrices of the state equations. The author expresses the feedback matrices with respect to the coefficient matrix of the state equation for a single-input and single-output feedback network, and shows how they are related to the poles and zeros of the transfer function. The author extends these concepts to multiple-input, multiple-output and multiple-loop feedback networks, and derives expressions for the return difference matrix and the null return difference matrix and relations of the zeros and poles of their determinants to the eigenvalues of the coefficient matrices under the nominal condition and under the condition that the elements of interest vanish