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：本文提出了稳定且鲁棒的线性参数变化状态空间（LPV-SS）模型的两种直接参数化方法。这些模型参数化方法能够先验地保证：在训练过程中，对于所有参数值，所允许的模型在收缩意义上是稳定的，或具有由用户定义值$\gamma$界定的Lipschitz常数。此外，由于参数化是直接的，因此可以使用无约束优化对模型进行训练。训练后的模型属于LPV-SS类别，这使得它们可应用于进一步的凸分析或控制器设计等场景。该方法在一个LPV辨识问题上的有效性得到了验证。