Tellegen's theorem and multivariable realizability theory†

By introducing a multivariable form of Tellegen's Theorem and a generalization of energy functions, the positive-real nature of immittance matrices of finite networks composed of resistors, p-plane inductors and capacitors, all non-negative, transformers and gyrators, is proven, us well as the lossless constraint. Multivariable reactance functions are investigated and the relation between such functions and multivariable Hurwitz polynomials is proved.