S domain transfer functions of full bridge inverter

Question

I need to design an inverter circuit as in the schema. It is driven by the unipolar PWM method. I have a problem with the circuit. It would be great if anyone can help me.

I want to get the s domain transfer function of the circuit from the duty cycle(reference voltage) to output voltage while consisting of the effect of the DC voltage source. So far I am not able to handle to linearize switching actions properly. I know how to do it in a more simple topology like buck or boost but here I am confused

^{simulate this circuit – Schematic created using CircuitLab}