This paper presents the robust linear quadratic regulator (LQR) control for the uncertain modular multilevel converters (MMCs). The classical LQR control prioritizes optimizing the performance index but lacks the ability to address converter uncertainties. This paper takes into account this limitation by developing a model of the MMC that considers parameter uncertainties. To enable LQR control in uncertain MMC systems, an optimization approach for the performance index employing linear matrix inequality (LMI) technique is proposed. Consequently, a novel robust control strategy for MMCs is established. The real-time performance of this LMI-based LQR control is evaluated against classical LQR control under both nominal and non-nominal conditions and single phase-to-ground fault using Opal-RT system. For this purpose, as the switching function model sufficiently captures all aspects of the MMC's behavior, the switching function model of the MMC is implemented on the Opal-RT OP4610XG system for real-time emulation of MMC. The results from real-time simulation of the system indicate that the proposed LMI-LQR method offers an advantage in robustness over the classical LQR method in presence of parameters uncertainty.