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Keywords:
Hurwitz polynomial; electrical networks
Hurwitz polynomial; electrical networks
Summary:
Homogeneous quadratic polynomials $f$ in $n$ complex variables are investigated and various necessary and sufficient conditions are given for $f$ to be nonzero in the set $\Gamma^{(n)}=\left\{z\in C^{(n)}:\text Re \ z>0\right\}$. Conclusions for the theory of multivariable positive real functions are formulated with applications in multivariable electrical network theory.
References:
[1] N. K. Bose: Problems and Progress in Multidimensional Systems Theory. Proc. IEEE, Vol. 65, No. 6, June 1977, pp. 824-840.
[2] M. Fiedler: Private communication, 1979. Zbl 0431.15005
[3] J. Gregor: Multivariable positive real functions. Res. Rep. III-3-1/3, 1978 (in Czech).
[4] T. Kоgа: Synthesis of finite passive N-ports with prescribed positive real matrices of several variables. IEEE Trans, on Circuit Th., Vol. CT-15, No. 1, March 1968, pp. 2-23. DOI 10.1109/TCT.1968.1082780
[5] M. A. Lavrentyev B. V. Shabat: Methods of the Theory of Functions of a Complex Variable. (in Russian). FIZMATGIZ, Moscow 1958.
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