This paper presents novel linear matrix inequalities (LMI)-based conditions to address the coprime factorization problem for polytopic linear parameter-varying (LPV) systems in both the continuous- and discrete-time cases. The proposed conditions rely on the use of homogeneous polynomial parameter-dependent (HPPD) matrix solutions of arbitrary degree g, which are used to obtain coprime factorization descriptions subject to time-varying parameters defined inside a polytopic structure with known vertices. For a given degree g, synthesis of right and left coprime factorizations in terms of two special state-feedback and filtering problems under quadratic performance are provided. Existence conditions are given from linear matrix inequalities relaxations based on an extension of Pólya's theorem and the HPPD approach. The effectiveness of the proposed conditions is evaluated by means of numerical examples.

中文翻译：

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基于齐次多项式方法的多面LPV系统的互质分解

本文提出了新的基于线性矩阵不等式 (LMI) 的条件，以解决连续和离散时间情况下多面线性参数变化 (LPV) 系统的互质分解问题。所提出的条件依赖于任意次数g的齐次多项式参数相关 (HPPD) 矩阵解的使用，这些解用于获得互质分解描述，该描述受在具有已知顶点的多面体结构内定义的时变参数的影响。对于给定的度g，二次下两个特殊状态反馈和滤波问题的左右互质分解合成性能提供。存在条件由基于 Pólya 定理和 HPPD 方法的扩展的线性矩阵不等式松弛给出。通过数值例子来评估所提出条件的有效性。