Design of controllers in the complex domain

The paper discusses a class of symmetric systems that can be reduced to systems with half the dimension and order, but with complex coefficients. Symmetric systems include doubly-fed induction machines, self-excited induction generators, three-phase converters, and three-phase active filters. The paper reviews general properties of symmetric systems in the state-space and frequency domains. Although complex models have been used in the literature in the past, few papers have considered their practical use, in particular for the direct design of controllers in the complex domain. The paper illustrates such a design in the case of a doubly-fed induction machine.