Partially linear additive models combine a linear component for some covariates with an additive nonparametric component for others, offering flexibility, interpretability, and the ability to include categorical variables in the linear part. Variable selection is critical to avoid including irrelevant covariates that reduce predictive performance. To address the impact of outliers and strong assumptions like second moments of the errors, a family of robust estimators is proposed. These estimators perform simultaneous variable selection for both model components. A simulation study demonstrates the advantages of the proposed method over its least-squares counterpart.