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algorithm arbitrary bounded real lemma capacitors circuit completely controllable completely observable compute defined eigenvalues entries excitation variables exists follows gyrators hybrid matrix inductors input lossless bounded real lossless positive real m x m matrix Z(s minimal realization minimum number network synthesis nondynamic network nonnegative definite nonreciprocal nonsingular nonsingular matrix nonzero normal rank number of reactive number of resistors obtained orthogonal matrix pole polynomial positive definite positive real impedance positive real lemma positive real matrix positive real Z(s prescribed problem of synthesizing rational functions reactance reactance-extraction reactive elements real lemma equations real rational realization F realization of Z(s reciprocal synthesis response variables result Riccati equation scalar scattering matrix solution solving spectral factor state-space equations state-space realization symmetric matrix synthesis of Z(s synthesis problem synthesis procedure technique terminated Theorem tion transfer function transfer-function matrix transformer vector Z(oo zero