This paper presents the analysis and design of a PWM nonlinear digital control of a buck converter based on input-output linearization. The control employs a discrete-time bilinear model of the power converter for continuous conduction mode operation (CCM) to create an internal current control loop wherein the inductor current error with respect to its reference decreases to zero in geometric progression. This internal loop is as a constant frequency discrete-time sliding mode control loop with a parameter that allows adjusting how fast the error is driven to zero. Subsequently, an outer voltage loop designed by linear techniques provides the reference of the inner current loop to regulate the converter output voltage. The two-loop control offers a fast transient response and a high regulation degree of the output voltage in front of reference changes and disturbances in the input voltage and output load. The experimental results are in good agreement with both theoretical predictions and PSIM simulations.