On multivariable half-plane analyticity and positive realness

A new set of necessary and sufficient conditions for positive realness of a rational multivariable function is derived. The conditions render correct results, whether or not there exist nonessential singularities of the first or second kind. The derivation of this set of conditions is based on necessary and sufficient conditions for a zero set of a rational function in a complex variable s depending on n complex parameters, to be confined to the closed left half complex plane. This latter set of conditions, in addition to a set of conditions where the confinement is to the open left half complex plane, are corollaries following a theorem which was published recently. These are stated without proof.