System matrices giving lossless positive-real transfer-function matrices

Let P(s) be a system matrix in first form giving rise to a transfer-function matrix G(s). It is proved that, if P(s) is system-equivalent to a lossless positive-real matrix, G(s) is lossless positive-real, while, if G(s) is lossless positive-real and P(s) has least order, P(s) is system-similar to a lossless positive-real matrix. The extensions to system matrices in second and third forms are given.