Coexistence of regular and chaotic behavior in the time-delayed feedback controlled two-cell DC/DC converter

This work deals with the behavior of the controlled two cell DC/DC converter. It has been reported in literature that the two-cell DC/DC converter may exhibit chaotic behavior under a badly tuned proportional controller. To stabilize the periodic orbit sank in the chaotic attractor we propose to apply the discrete time-delayed feedback controller. We first present conditions of stability using the Lyapunov theory. Next, we investigate the coexistence of a chaotic attractor and a regular behavior in a particular region of the parameter space. Finally, we attempt to bring some theoretical explanation to the coexistence of attractors approved by numerical simulations in which we depict the sensitivity of the attractors to the initial condition.