Transfer Function of a boost converter
To determine the transfer function of a switching converter, there are different ways. The state space averaging technique or SSA has been introduced by Dr. Cuk in 1976 and heavily uses matrix analysis. The principle is to weight the coefficients describing the circuit on- and off-states by \$D\$ and \$(1-D)\$ to form a time-continuous nonlinear equation. You then need to linearize this expression and assemble a canonical model. Then, you can apply your favorite tools to determine the control-to-output transfer function of your choice. The problem with the SSA is that it models the entire converter: should you want to add a front-end filter or add a parasitic term to the capacitor or the inductor, you have to restart from scratch.

In 1986, Dr. Vorpérian came up with the PWM switch model, an elegant way to model the switching cell alone, leaving the rest of the elements untouched. The cell is invariant and can be plugged in any 2-switch converter. The original paper is available here and an introduction with associated auto-toggling DCM-CCM models is described here. The principle is easy, identify the switching cell and replace the symbol by the linearized PWM switch as shown below:



The recent APEC 2018 seminar "Closing the Feedback Loop through Simulation and Analysis" available here shows how to determine the control-to-output transfer function of the boost converter operated in voltage mode. The expression features a LHP zero and a RHP zero. The denominator is a of second order in continuous conduction mode or CCM. It is determined in the PPT using the fast analytical circuits techniques or FACTs:



Should you want to determine the function, you have all the elements to give a try and even explore the discontinuous mode of operation (DCM) if you want.