Stability analysis and control of bifurcations of parallel connected DC/DC converters using the monodromy matrix

The paper studies the stability of parallel DC/DC converters using the concept of monodromy matrix (the state transition matrix for one complete cycle), whose eigenvalues are the Floquet multipliers. This matrix is composed of the state transition matrices for the smooth intervals and those across the switching events (called saltation matrices). We show that instabilities in this system can be caused by smooth as well as nonsmooth period doubling bifurcations, the latter occurring when the fundamental solution matrix undergoes a discontinuous jump as a periodic solution touches a non-smooth hyper-surface of discontinuity. Based on the expression for the saltation matrices (the state transition matrices across switching events) we propose new controllers that can stabilize the period-1 operation by keeping the eigenvalues inside the unit circle.