Discrete-time modelling and robust analysis of a buck converter

A discrete-time state-space representation of a Buck converter is presented. This analytical state-space model provides explicit insight on how circuit parameters influence the stability and transient performance for this converter type. Variations in the power rail components and parasitic resistances are accommodated, which are typically neglected in compensator synthesis for switched mode power supplies. With this representation, robust stability and feedback performance can be readily assessed. Moreover, the model can be employed directly for the design of digital robust compensators, and it provides a basis for the development of compensators in analytical form rather than the use of numerical discretisation techniques.