The real part of a multivariable positive real function and some applications

A method of generating a multivariable positive real function (MPRF) from the given multivariable real part is presented. The constraints on the given real part, in addition to its nonnegativeness, are studied so that an MPRF can be generated in general. Some particular cases are studied in greater detail. By extending the Strum test to two-variable functions, a procedure for testing the nonnegativeness of a two-variable real part is presented. A transformerless synthesis technique for the realization of a class of two-variable positive real functions is given.