In recent years, power systems have evolved in physical and cyber-physical layers. In the physical layer, the changes are motivated by environmental concerns resulting in the integration of new types of generation/demand/storage into the grid. These integrations offer the opportunity of forming self-sufficient microgrids. Based on the hierarchical microgrid control structure, it should provide a high-performance low-level control while damping the high-frequency oscillations. Moreover, it should share power among DGs at the primary level and restore voltage/frequency at the secondary level. However, achieving these objectives is challenging because of factors such as lack of inertia, system complexity, different line characteristics, high-frequency modes of switching converters and their filters, delay, and incomplete communication graph. With the advent of smart grid technologies, the cyber-physical layer of the grid has transformed, and more measurement data are available. These data are mostly used for monitoring, metering, and protection. This thesis tries to bridge the gap between measurement data and high-performance control design for microgrids to address their operational challenges. The scope of this thesis covers up to the secondary control level. At the lowest level, the passivity theory has been used to tackle the problem of high-frequency oscillation between converters in a decentralized way. To this end, conditions of data-driven robust passivity for a performance channel are proposed. This method is used to make the input admittance of an AC grid-connected converter passive while the tracking performance is optimized. To validate the performance of designed controllers with high fidelity, an experimental Hardware-in-the-Loop (HIL) setup is developed and extended to a Power-HIL (PHIL) setup. However, PHIL tests have a performance limitation due to their stabilization. A data-driven method is proposed to optimize their performance while robust stability is guaranteed. This PHIL setup is employed for the validation of the passivity-based converter control. In addition, inspired by railway system standards, conditions for data-driven partial positive realness over an arbitrary frequency set are developed and used for the traction converter control design. Moreover, the primary/secondary microgrid control problem is formulated as a comprehensive data-driven multivariable synthesis problem. In this method, active power-sharing and frequency/voltage restoration are optimized while the closed-loop stability with a predefined margin is guaranteed. Due to the fixed structure, the controller can be designed based on the available communication while considering its delay. Since there is no need for time-scale separation between primary and secondary, this method leads to better performance. Moreover, because of data-driven property and multivariable structure, there is no need for decoupling or any assumption on the grid impedance. This design is extended to reactive power sharing using the spare capacity of PhotoVoltaics (PVs). In addition, a data-driven Linear Parameter Varying (LPV) multivariable synthesis method is proposed and used for the microgrid control to extend the applicability in different operating points. All the proposed methods are in a data-driven framework, which is suitable for complex power system applications. As well, the design problems are in convex programming form, which can be solved efficiently.