Improved M-matrix condition for the existence of positive-real weighting (Q1059036)

It is proved that, for a given stable transfer matrix G(s), there exists a constant diagonal matrix W which makes WG(s) positive-real if \(Re g_{ii}(j\omega)\geq 0\) and I-\(\epsilon\) is an M-matrix where \(\epsilon =(\epsilon_{jk})\) is defined by \(\epsilon_{ii}=0\) and \(\epsilon_{jk}=\sup_{\omega}| g_{ik}(j\omega)| /\{Re[g_{ii}(j\omega)]\cdot Re[g_{kk}(j\omega)]\}^{1/2}.\)