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This paper presents the modeling and control of active front-end (AFE) converters using complex state-space representation, a technique developed and thus far mostly employed for the analysis of ac machines. Particularly, three-phase PWM voltage-source and current-source rectifiers are thoroughly studied using the graphical capabilities of this approach, namely, complex signal flow graphs. These are used to directly and intuitively derive high-performance nonlinear control laws based on input-output feedback linearization. Specifically, a cascaded and a paralleled control scheme are investigated for the voltage-source rectifier, whereas a cascaded scheme is considered for the current-source rectifier. Under these strategies both converters exhibit linear and decoupled d-q axes dynamics, while also attaining a reactive power compensation capacity. Moreover, linearization of their respective dc-link voltage and current loops utterly enforces and ensures their operating stability. All this is achieved without the elaborate mathematical complexity of input-output linearization, effectively shunned out by the proposed complex state-space approach. Finally, experimental results from 5-kVA digital-signal-processor-based laboratory prototypes verify the analysis and downright performance evinced by these AFE converters.