This paper presents a robust passivity‐based control (RPBC) strategy for half‐wave zero‐voltage switching quasi‐resonant (HW‐ZVS‐QR) buck and boost type converters. The proposed controller is based on energy shaping and damping injection. Theoretical analysis shows that the resulted closed‐loop HW‐ZVS‐QRs are globally asymptotically stabilised even if the physical constraint on the magnitude of the control signal is taken into account. Also, an integral function of the output error is added into the feedback path of the conventional passivity‐based control design. As a result, such controller not only offers a global asymptotic stable operation but also provides strong robustness to a wide range of parameter mismatch. It is also demonstrated that the proposed controller stabilises the converter in cases where the widely used linear multiloop controller fails. Finally, some simulation and experimental results comparing the performance of the proposed RPBC with that of the conventional linear multiloop controller are presented.