Lyapunov-based robust controller design for single-inductor dual-output buck converters using sum of squares programming

In this paper, the design process of a stabilizing controller for the single-inductor dual-output (SIDO) buck converter is described. A quadratic Lyapunov function is considered to evaluate the stability of the system and the controller's coefficients are designed in a way that the decrease in the Lyapunov function in each time step is guaranteed. To certify this condition, the design algorithm exploits the ability of sum of squares programming tools in proving the non-negativity of polynomial functions. An integral action, on the tracking error of desired states, is implemented in the control loop in order to provide a robust output regulation in case of load changes and model parameter uncertainties. An optimization based algorithm is proposed which maximizes the region of attraction while designing the stabilizing controller. The proposed controller design method is evaluated through simulations of detailed switching model of a SIDO buck converter.