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且robust的线性参数时变状态空间 (LPV-SS) 模型的直接参数化形式。这些模型参数化形式保证了在训练过程中的所有参数值下，所允许的模型在收缩意义下是稳定的，或者具有用户定义的Lipschitz常数上限$\gamma$的bound。此外，由于这些参数化形式是直接的，所以这些模型可以使用无约束优化进行训练。由于训练出的模型属于LPV-SS类，因此它们在凸分析或控制器设计等方面非常有用。本文通过一个LPV模型识别问题展示了该方法的有效性。