This paper presents two direct parameterizations of stable and robust linear parameter-varying state-space (LPV-SS) models. The model parametrizations guarantee a priori that for all parameter values during training, the allowed models are stable in the contraction sense or have their Lipschitz constant bounded by a user-defined value $\gamma$. Furthermore, since the parametrizations are direct, the models can be trained using unconstrained optimization. The fact that the trained models are of the LPV-SS class makes them useful for, e.g., further convex analysis or controller design. The effectiveness of the approach is demonstrated on an LPV identification problem.

翻译：本文提出了两种稳定的鲁棒线性参数变化状态空间（LPV-SS）模型的直接参数化方法。这些模型参数化方法先验地保证：在训练过程中的所有参数取值下，所允许的模型在收缩意义上保持稳定，或将其利普希茨常数限制在用户定义的阈值 $\gamma$ 以内。此外，由于采用直接参数化方式，这些模型可通过无约束优化进行训练。训练后的模型属于LPV-SS类别，使其适用于如进一步的凸分析或控制器设计等场景。通过LPV辨识问题，验证了该方法的有效性。