Generating Series for Interconnected Analytic Nonlinear Systems
Generating Series for Interconnected Analytic Nonlinear Systems
复制标题
互连解析非线性系统的生成级数
DOI：
10.1137/s036301290343007x
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
Yaqin Li
中科院分区：
文献类型：
--
作者：
W. Gray;Yaqin Li
给定两个用 Fliess 算子表示的解析非线性输入输出系统，在统一设置中考虑四种系统互连：并联连接、乘积连接、级联连接和反馈连接。在每种情况下，都会产生相应的生成级数，并给出相应 Fliess 算子的收敛条件。在此过程中，形式幂级数的组合积的现有概念显着扩展了其已知属性集。此外，形式幂级数的反馈乘积的概念在广泛的背景下得到了很好的定义，并且描述了其基本属性。
Given two analytic nonlinear input-output systems represented as Fliess operators, four system interconnections are considered in a unified setting: the parallel connection, product connection, cascade connection, and feedback connection. In each case, the corresponding generating series is produced and conditions for the convergence of the corresponding Fliess operator are given. In the process, an existing notion of a composition product for formal power series has its set of known properties significantly expanded. In addition, the notion of a feedback product for formal power series is shown to be well defined in a broad context, and its basic properties are characterized.