Positive Real Functions of Several Variables and Their Applications to Variable Networks

This paper is concerned with networks containing variable parameters. The concepts of multivariable positive real function, multivariable reactance function, and multivariable positive real matrix are introduced, and it is shown that these concepts are useful for dealing with a wide class of variable parameter networks. Several theorems on these functions are established. Extensions of several conventional procedures of circuit theory are presented for the synthesis of such networks and their limitations are discussed. The last section concludes with a discussion of the approximation problem of networks with one variable parameter.