Cross regulation is the main technical drawback 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 openloop shaping of the Multi-Input Multi-Output (MIMO) systems. The control design procedure includes: (i) determination of the non-parametric model of a SIDO buck converter at its rated operating point, (ii) determination of the class of the controller, and (iii) converter open-loop shaping by convex minimization of the square second norm of the error between the converter openloop transfer function and a desired open-loop transfer function. The proposed controller minimizes the coupling between the outputs of the SIDO buck 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.