Switching Control Strategy for DC–DC Converters Based on Polynomial Lyapunov Function and Sum-of-Squares Approach

The introduction of switched system theory opens new perspectives for the control design of dc/dc converters. Regarding the classical two-level converters, two switching control design methodologies have been developed based on the common quadratic Lyapunov function (CQLF) or piecewise quadratic Lyapunov function (PQLF). However, the CQLF-based design method is not applicable for the multilevel dc/dc converter (MC). As for the PQLF-based design method, it encounters the problem that the control design is very complex, involving a nonlinear optimization problem. To further advance the application of the switching system theory in power converters, a design framework based on the polynomial Lyapunov function and the sum-of-squares approach is proposed in this article. The proposed design method generalizes the CQLF-based one. Moreover, compared with the PQLF-based design method, the mathematical design procedure can be significantly simplified. Experimental validations on an MC, i.e., the three-level flying capacitor converter and a two-level Buck-Boost converter illustrate the versatility and the effectiveness of the proposed design framework. Moreover, comparative tests show the good control performance of the designed switching control strategy. The currently presented works are preliminary but could constitute an interesting direction for developing control solutions of power converters.