I have looked into a model like this long time ago. It was when the first PWM controllers having frequency foldback in light-load conditions were released. As the loop was going through different operating modes, it was important to check stability in all these loading conditions. One mode was when the peak current was frozen while the frequency was controlled through a voltage-controlled oscillator (VCO).
Most of the available small-signal models imply a fixed operating frequency where the error voltage controls either the duty ratio directly (voltage-mode control) or the inductor peak current (current-mode control). In continuous conduction mode (CCM), the transfer function and the dc transfer characteristic ignore the switching frequency and load values (ideal model). In discontinuous conduction mode (DCM), the switching frequency plays a role as well as the loading conditions for determining the output voltage. As thus, controlling the output via the switching frequency is a possibility if you freeze the peak current as in the previously-described example.
For many years now, I have adopted the PWM switch model to analyze power converters. Released in 1986 by Vatché Vorpérian, it cannot be beaten in terms of simplicity of analysis. The below figure shows you in the left side the PWM switch operated in peak-current-mode control with \$V_c\$ the control voltage. In all the equations, the frequency is fixed. In the right side, the model is tweaked to unveil the switching frequency contribution:
The difficulty now is to derive a small-signal approach with this large-signal model. This is not the place to show the complete linearization steps but I did it for the flyback converter exercise, look here. The model is invariant and you can reuse it in a buck converter. You first start with the large-signal model with equations reworked for future linearization:
When this is done, you start the linearization of the PWM switch operated in variable frequency. This is not a simple thing to do and the right-side window shows the many coefficients to determine:
When you have confirmed your model is correct, then you insert it in the buck configuration and you start the analysis using for instance the fast analytical circuits techniques or FACTs as described in my new book entirely dedicated to small-signal analysis of switching converters. I have covered many switching cells but did not touch variable frequency - except for the LLC converter - because it is rarely used as a control means.