This thesis explores the cause of the occurrence of such limit cycle oscillations and their suppression in a couple cascaded DC-DC converters systems using the concepts of nonlinear dynamics and bifurcation theory, in particular, the amplitude death (AD) phenomena. AD is a well-known mathematical phenomenon characterizing the coupling-induced stabilization of several interconnected nonlinear oscillatory systems. It has been discussed that AD-based solutions can be used to stabilize DC DPSs under various coupling schemes. These have been demonstrated here through numerical simulations and experimental validations. Numerical results reveal that if heterogeneity (e.g., the system parameters are mismatched) is introduced in coupled oscillatory systems, AD can happen. However, in some situations, when internal parameters of the systems are not accessible to the user, AD can only happen if an instantaneous delay is introduced. It has been found that adding a dynamical coupling - where the coupling link has its dynamical properties - is a replacement of delay circuits and that can lead the coupled identical and nonidentical oscillating systems to a steady-state equilibrium point through AD phenomena.
To do so, the stability of the equilibrium solution is analyzed for coupled converters systems using the averaged differential equations near a supercritical Hopf bifurcation. Death regions are identified for asymptotic stability under different coupling conditions. It is shown that the largest eigenvalue obtained from XPPAUTO completely characterizes the effect of connection configuration on the stability of diffusively coupled identical and nonidentical systems. In particular, all identical systems have no death regions regardless of the type of couplings. Furthermore, identical converters systems with delay, dynamical or relay coupling, or non-identical systems with any type of coupling, respectively. The results further characterize the different coupling configurations as the mechanism for the death of coupled oscillators near Hopf bifurcation. Also, some generalizations are given for converters networks with LRC-type coupling.