Border-Collision Bifurcations in a DC/DC Converter with Multilevel Pulse-Width Modulation

Considering a pulse-width modulated DC/DC converter as an example, this paper describes a border-collision bifurcation that can lead to the appearance of quasiperiodicity in piecewise-smooth dynamical systems. We demonstrate how a two-dimensional torus can arise from a periodic orbit through a bifurcation in which two complex-conjugated Poincare characteristic multipliers abruptly jump from the inside to the outside of the unit circle. The torus may be ergodic or resonant. In both cases, however, the diameter of the torus develops approximately linearly with the distance to the bifurcation point as opposed to the characteristic parabolic form of the well-known Neimark-Sacker bifurcation.