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This paper proposes a multivariable digital control design methodology for the voltage regulation of an islanded single distributed generation (DG) unit microgrid and its dedicated load. The controller design methodology is based on a family of spectral Multi-Input Multi-Output (MIMO) models of the microgrid system and performs open-loop shaping and system decoupling simultaneously by a convex optimization approach. The control design procedure includes: (i) the determination of a family of nonparametric models of the system at various operating points, (ii) the determination of the class of the controller, and (iii) system open-loop shaping by convex minimization of the summation of the square second norm of the errors between the system open-loop transfer functions and a desired open-loop transfer function. Based on the proposed design methodology, two dq -augmented voltage controllers are proposed to regulate the load voltages of a single-DG-unit microgrid. The proposed controllers guarantee the robust stability and satisfactory dynamic response of the system in spite of load parametric uncertainties and also the presence of nonlinear load. This paper describes the theoretical aspects involved in the design procedure of the controllers and evaluates the performance of the controllers based on simulation studies and experiments.