On the robustness of the DC-DC boost converter under washout SMC

In this paper, the stability and robustness of the classical DC-DC boost converter operating in Discontinuous Conduction Mode (DCM), when controlled by washout Sliding Mode Control (SMC), are revisited. It is shown that there is an unstable limit cycle in the sliding dynamics due to a subcritical Hopf bifurcation. This limit cycle surrounds the stable pseudo-equilibrium on the sliding plane, bounding the attraction basin of such equilibrium for the sliding dynamics. The existence of this limit cycle and its evolution with parameters turn out to be of great importance for the stability and robustness control of this type of power converter.