Rich non-linear phenomena, such as Neimark-Sacker bifurcation and chaos and so on, are proven to exist and cause instability in one-cycle controlled (OCC) buck-boost converters. This paper presents a composite function embedded method based one-cycle control (CFOCC) to resolve such problems. By modifying the conventional OCC through embedding a composite function, the non-linear stability performances of the system are considerably improved to avoid bifurcation phenomena and the stable region is enlarged. Further, various commonly used functions, such as the logarithmic function, the arc-tangent function, etc., can be used as the embedded composite functions. The effectiveness of the proposed control method is verified by simulation and experiment. [ABSTRACT FROM AUTHOR]