Switched Dynamical Systems with Double Periodic Inputs: An Analysis Tool and Its Application to the Buck-Boost Converter

This paper considers a class of switched dynamical systems to which two periodic inputs are applicable. We derive a one-dimensional (1-D) return map and its derivative analytically for arbitrary shapes of the inputs. Based on the derivative, we introduce a slope chart that displays the relationship between the slope of the return map and that of the inputs. Applying the slope chart to a simplified model of the buck-boost converter (SBBC) with two periodic triangular inputs, we obtain a sufficient condition for chaos generation and that for the stability of the periodic behavior. The conditions guarantee that the first input can cause chaotic or periodic behavior and that the second input can change from chaotic behavior into periodic behavior and vice versa. A circuit model of the system is also proposed and the periodic and chaotic behaviors are demonstrated in the laboratory.