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This Thesis addressed the challenge of ensuring balanced currents in the phases of a multi-kW, interleaved dc-dc converter by means of closed-loop digital control. The Thesis examines uniformly-sampled, valley-current, peak-current and average-current control for a dual interleaved boost converter with inter-phase transformer which might form part of the power train of an electric vehicle. Also, an enhancement of the average-current control is investigated in which the transistor duty-ratio is updated more rapidly, which allows an improvement of approximately ten times in the response speed of the system. Based on the theoretical analysis, the average-current control methodology was determined to be the most suitable technique for this type of converter as it ensures well-balanced phase currents over a wide range. To provide a basis for control system analysis and design for interleaved converters, a modelling methodology is developed based on a combination of multi-rate data-sampled theory and a small-signal averaged converter model. The model is shown to represent accurately the interaction between the interleaved phases, revealing a reduced stability range compared with a non-interleaved converter. The modelling and control methods are validated using switched and average value simulations obtained with the SABER software and by experimental results from a 25 kW, 30 kHz converter prototype. The control techniques were implemented on a Texas Instruments TMS320F28335 digital signal controller.