To satisfy the requirements of accurate and robust decision-making in classification tasks with noisy and redundant features, and to enhance the model applicability in abnormal data scenarios, we propose a Robust Geometric Twin Support Vector Machine (RGTSVM) that integrates the RoBoSS robust loss and L1 penalty term.Firstly, the noise-insensitive RoBoSS robust loss is adopted to replace the traditional hinge loss, which reduces noise interference and improves the model robustness; meanwhile, the L1 penalty term is utilized to realize feature selection and effectively eliminate redundant features. Secondly, to solve the non-convex and non-smooth optimization problem of the model, we design a solution algorithm based on proximal gradient descent, which achieves efficient parameter updating through soft-threshold iteration. Furthermore, a theoretical analysis is conducted based on the influence function to reveal the robustness of the model under sample perturbations. Finally, experiments are carried out on synthetic datasets and UCI benchmark datasets, and the proposed RGTSVM is compared with a variety of comparative methods under label noise interference and resampling noise. The results show that the proposed model achieves the best classification performance and high feature recognition accuracy.This study proves that integrating robust loss and sparse penalty terms into twin support vector machines can effectively improve the model applicability in abnormal data scenarios, and provides a novel and effective modeling scheme for control decision-making in complex scenarios.