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This paper presents a robust control synthesis framework for switched DC-DC converters. The framework is based on an LMI formulation which can be solved automatically by efficient convex optimization algorithms. The method considers parameter-dependent Lyapunov functions such that it can take into account the uncertainty of converter parameters, nonlinear dynamics (such as state-dependence), as well as transient and steady-state performances that can be imposed beforehand. The result of the proposed synthesis method is a gain-scheduled controller that guarantees stability despite the accounted nonlinear dynamics and can provide excellent performances. Two different synthesis examples are shown for a DC-DC boost converter and their performance and robustness are compared with a standard control approach as current-mode control, both in nominal and non-nominal conditions. Finally, the proposed approach is verified with experimental results.