Electrocardiogram (ECG) signal exhibits inherent uniqueness, making it a promising biometric modality for identity authentication. As a result, ECG authentication has gained increasing attention in recent years. However, most existing methods focus primarily on improving authentication accuracy within closed-set settings, with limited research addressing the challenges posed by open-set scenarios. In real-world applications, identity authentication systems often encounter a substantial amount of unseen data, leading to potential security vulnerabilities and performance degradation. To address this issue, we propose a robust ECG identity authentication system that maintains high performance even in open-set settings. Firstly, we employ a multi-modal pretraining framework, where ECG signals are paired with textual reports derived from their corresponding fiducial features to enhance the representational capacity of the signal encoder. During fine-tuning, we introduce Self-constraint Center Learning and Irrelevant Sample Repulsion Learning to constrain the feature distribution, ensuring that the encoded representations exhibit clear decision boundaries for classification. Our method achieves 99.83% authentication accuracy and maintains a False Accept Rate as low as 5.39% in the presence of open-set samples. Furthermore, across various open-set ratios, our method demonstrates exceptional stability, maintaining an Open-set Classification Rate above 95%.