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This article proposes a design procedure for $\mathcal {H}_{\infty }$ current controllers suitable for application in grid-connected converters (GCCs) subject to disturbances and uncertain parameters. Linear matrix inequalities provide robust state feedback controllers from a set of design parameters automatically tuned with the help of a genetic algorithm, oriented by a suitable objective function. Such strategy allows to overcome the problem of $\mathcal {H}_{\infty }$ high control gains, ensuring a good tradeoff between performance and robustness against uncertain grid parameters. The proposal contributes to improve the effective use of metaheuristics for automated control tuning in GCCs, avoiding time-consuming human–machine interaction in the design stage. A case study with experimental results is presented, demonstrating the viability and the superior performance of the proposed controllers with respect to similar techniques, and also the compliance with the IEEE 1547 Std for grid currents. [ABSTRACT FROM AUTHOR]