发表机构
Chapman University; Ben-Gurion University of the Negev（查普曼大学; 内盖夫本古里安大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对与绝对稳定性相关的典范超正函数，引入其系统参数化方法，证明其为超正函数凸集的极点，相关结论在两种框架下成立，技术上借助二次矩阵包含关系简化分析。
AI 中文摘要
在线性时不变框架中，无源系统由正实函数建模，耗散系统可由定量超正实函数的子集建模，这类函数通过嵌套包含关系关联，该函数族已在作者此前的三篇工作中被引入和研究。本文进一步聚焦于典范超正函数的真子集，尽管该函数族“规模较小”，但其研究具有充分动机：首先，该集合与绝对稳定性（Lurie问题）相关；其次，本文引入了所有典范超正函数的系统参数化方法；此外，每个典范超正函数均可视为超正函数凸集的一个极点，具体而言，典范超正函数的凸组合是超正函数，但非典范。这些结论在解析函数和状态空间实现阵列两种框架下均成立。技术上，利用矩阵及矩阵值有理函数的二次矩阵包含关系可简化部分分析。
英文摘要
In the linear time-invariant framework, passive systems are modeled by positive real functions. Dissipative systems can be modeled by the subset of quantita- tively Hyper-positive real functions, related through nested inclusions. This family was introduced and studied in our three previous works. Here, we further focus our attention on the proper subset of canonical Hyper-Positive functions. Although this family is "small", its exploration is well motivated: First, this set turns to be associated with absolute stability (the Lurie problem). Then, a systematic parametrization of all canonical Hyper-Positive functions is introduced. Moreover each canonical Hyper-Positive function can be viewed as an extreme point of the convex set of Hyper-Positive functions. Specifically a convex combination of canonical Hyper-Positive is Hyper-Positive, but not canonical. These observations hold in both frameworks: of analytic functions and of state-space realization arrays. Technically, some of the analysis is facilitated by employing Quadratic Matrix Inclusions of both, matrices and of matrix-valued rational functions.
