Power electronic converters are time-varying, nonlinear dynamical systems. They exhibit a wide range of steady-state responses. The desired behaviour is a stable periodic motion around a predefined value with a frequency that is equal to that of the external clock. However, as parameters vary the operation can lose stability and go from one regime to another. Such phenomena are termed bifurcations and can degrade the output performance of the converter. Hence, it is of practical importance to know the conditions that cause such bifurcations to occur and to design the system so that it operates in the desired region. In the past, engineers have typically analysed the stability of power electronic systems by linearising the model about a fixed point. This captures the low-frequency properties while ignoring the detailed dynamics occurring at frequencies higher than the external clock. However, the demand for better functionality, reliability and performance means an in-depth analysis into the complex behaviour exhibited by dc-dc converters is required. Traditionally, dc-dc converters are employed with analog controllers whose function is to regulate the circuit. With advances in technology, digital control has become a potentially advantageous alternative to analog control. One of the main advantages of digital control is the ability to design more sophisticated design strategies to enable high performance dc-dc converters e.g. digital state-feedback control. Unfortunately, little work exists in the area of the effect of noise on digital control. This is a field that requires intensive study as to completely understand the nonlinear dynamics so as to enable accurate and economic designs. The aim of this thesis is to address these issues through the application of advanced nonlinear mathematics. The stability of power electronic systems is assessed with a view to developing design guidelines in order to ensure stable operation over a wide operating region.