In this article, multivariable control strategies are developed for a three-level flying capacitor buck DC-DC converter, tailored for electric vehicle powertrain applications. The work presents a linearization of the Continuous Time Averaged Model of the converter in state space and transfer function matrix. Additionally, it introduces a multi-input multi-output control time-domain design using a Linear Quadratic Integral approach based on this linearized model. Further, a frequency-domain design for structured multi-input multi-output control is proposed, utilizing H-infinity loop-shaping derived from a mixed-sensitivity approach. Each methodology is elaborated with corresponding simulation results, showcasing the effectiveness of the control strategies. The paper methodically progresses from model development and linearization through control design and performance analysis, providing a thorough examination of the dynamic control of the converter, and its capabilities within a multivariable framework.