Cross regulation is the main technical challenge of a Single-Inductor Multiple-Output (SIMO) dc-dc converter. This paper proposes a multivariable digital controller to suppress the cross regulation of a Single-Inductor Dual-Output (SIDO) buck converter in Continuous Conduction Mode (CCM) operation. The controller design methodology originates from the open-loop shaping of the Multi-Input Multi-Output (MIMO) systems. The control design procedure includes: (i) determination of a family of nonparametric models of the SIDO converter at operating points of interest, (ii) determination of the class of the controller, and (iii) system open-loop shaping by the convex minimization of the summation of the square second norm of the errors between the system open-loop transfer function matrices and a desired open-loop transfer function matrix. The proposed controller minimizes the coupling between the outputs of the SIDO converter and provides satisfactory dynamic performance in CCM operation. This paper describes the theoretical aspects involved in the design procedure of the controller and evaluates the performance of the controller based on simulation studies and experiments.