Supercapacitors are well suited for braking energy recovery in electrical drive applications and for voltage sag compensation. For voltage-sensitive devices, only a small voltage deviation can be acceptable, and therefore the voltage controller should be fast. This paper analyzes the design of such a controller for DC bus voltage stabilization considering a GaN transistor-based converter with a 400 kHz switching frequency. Inner and outer loop controller design considering delays caused by the digital nature of the controllers has been analyzed in the paper. This paper proposes to use adaptable controller for the outer voltage loop, thus increasing the stability and reducing the calculation time. The 2p2z controller has been developed for the current loop, achieving a 20 kHz bandwidth and a response time of less than 0.2 ms. A 2p2z controller with adaptable coefficients has been developed for the outer voltage loop, achieving a 2 kHz bandwidth and a response time of 2 ms. Voltage controller digital implementation is split into two switching cycles, thus decreasing the required time for current and voltage control loops implementation from 2.1 µs to 1.5 µs. This allows calculating three current control loops for three-phase interleaved converter control. By combining such three-phase converters in parallel, it is possible to develop modular six-, nine-, or even more-phase interleaved DC-DC converters for high-current applications.