Flexible polyhedral Lyapunov functions for the robust constrained stabilization of bilinear boost DC-DC converters

Abstract

Recent research efforts, relying on constrained stabilization principles, have been concentrated on the design of robust and efficient state-feedback control laws for switched-mode DC-DC boost converters, characterized by accurate nonlinear dynamics incorporation, nonconservative handling of hard state and control constraints, and robustness to supply voltage variations and load changes. This paper focuses on the efficient construction of flexible polyhedral Lyapunov functions, which can facilitate control design procedures which address all aforementioned issues via the generation of contractive polytopes (safety domains). New non-conservative conditions for the averaged-model bilinear converter dynamics and a corresponding ray-gridding algorithm are proposed that allow near-maximal approximations of the real stability domains with negligible computational cost. A significant improvement in the size of the contractive domains is obtained by resorting to more flexible partial contractivity conditions. This novelty allows the extension of the constrained stabilization framework to robust constrained tracking, whereby a wide operating region may be covered. The proposed ideas can be applied for the specification of affine state-feedback control laws and are numerically evaluated on a boost converter example using the exact switched model of the converter.