State-space properties of real rational J-lossless matrices and their applications to network synthesis

A system criterion is given for a real rational n × n matrix S(p) to be J lossless for a given J, i.e. J-S~*(p)JS(p)¿ 0 in Re p > 0 and J-S~(-p)JS(p) = 0 where J = J~ and J2 = In. This algebraic property is then applied to the synthesis of lossless-chain and chain-scattering matrices and to stable transfer-matrix functions by cascade load and cascade networks using the minimum number of reactive elements.