Root locus rules for polynomials with complex coefficients

Applications were found recently where the analysis of dynamic systems with a special structure could be simplified considerably by transforming them into equivalent systems having complex coefficients and half the number of poles. The design of controllers for such systems can be simplified in the complex representation, but requires techniques suitable for systems with complex coefficients. In the paper, the extension of the classical root locus method to systems with complex coefficients is presented. The results are applied with some advantages to a three-phase controlled rectifier.