Chen-Fliess级数的加法网络：局部收敛性和相对度
Additive Networks of Chen-Fliess Series: Local Convergence and Relative Degree
摘要：
给定一个输入输出系统的可加网络，其中网络的每个节点都用局部收敛的Chen-Fliess级数来表示，建立了网络的两个基本性质。首先，它表明，每个输入输出映射之间的一个给定的节点对有一个局部收敛的Chen-Fliess级数表示。第二，充分条件下，一对节点之间的输入-输出映射有一个定义良好的相对程度所定义的生成系列。通过分析得出结论，这种相对度性质在一定意义上是通有的。
英文摘要：
Given an additive network of input-output systems where each node of the network is modeled by a locally convergent Chen-Fliess series, two basic properties of the network are established. First, it is shown that every input-output map between a given pair of nodes has a locally convergent Chen-Fliess series representation. Second, sufficient conditions are given under which the input-output map between a pair of nodes has a well defined relative degree as defined by its generating series. This analysis leads to the conclusion that this relative degree property is generic in a certain sense.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
