A generalization of Darlington theorem for real positive \(J\)-symmetric matrix-functions (Q1896843)

An old result of \textit{S. Darlington} [J. Math. Phys. 18, 257--253 (1939)] on linear fractional representations for rational real positive functions has found many applications in the analytic theory of networks. The present author extends these ideas to obtain a linear fractional representation for rational real positive \(J\)-symmetric matrix functions of order \(n\), where \(J= \left(\begin{smallmatrix} I_r & 0\\ 0 & I_s\end{smallmatrix}\right)\), where \(I_r\) is the identity \(r\times r\) matrix and \(r+ s= n\).