We elucidate a class of pulse soliton-based model stabilized control for Cuk converter with synchronous circuit, where the pulse soliton exists between two consecutive instant compensation moments. Based on the pulse control theory and Razumikhin-Type stability criteria, the sufficient conditions for the global exponential stability of the Lyapunov function are obtained. Afterwards, the theoretical results are applied to the synchronous control of the Cuk converter system, which illustrates the applicability of the proposed pulse soliton control scheme. The simulation results show that, under certain conditions, swift transient response and excellent stability of the Cuk converter can be realized by the synchronous control circuit of the pulse soliton.