Consider a set of single-input, single-output nonlinear systems whose input-output maps are described only in terms of convergent Chen-Fliess series without any assumption that finite dimensional state space models are available. It is shown that any additive or multiplicative interconnection of such systems always has a Chen-Fliess series representation that can be computed explicitly in terms of iterated formal Lie derivatives.

中文翻译：

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为 Chen-Fliess 系列的网络生成系列

考虑一组单输入、单输出非线性系统，其输入输出映射仅根据收敛的 Chen-Fliess 级数来描述，而没有任何有限维状态空间模型可用的假设。结果表明，此类系统的任何加法或乘法互连始终具有 Chen-Fliess 级数表示，可以根据迭代形式 Lie 导数进行明确计算。