AI 中文总结
本文针对多输入线性集合系统的结构平均可控性问题，在单输入情形已完全刻画的基础上，给出一般多输入情形的完整充要条件，即除可达性外，核心需存在行饱和匹配。
AI 中文摘要
我们研究多输入线性集合系统的结构平均可控性问题，该问题关注某稀疏模式是否能构成平均可控的线性集合系统。单输入情形已被完全刻画，但一般多输入情形仍未解决。本文对一般多输入情形给出完整刻画，证明集合系统结构平均可控的充要条件除可达性外，还需其核心（与系统关联的无环子图，在单输入情形的结果中起核心作用）存在行饱和匹配。
英文摘要
We study structural averaged controllability for multi-input linear ensemble systems. In this problem, one asks whether a sparsity pattern admits a linear ensemble system that is averaged controllable. The single-input case has been characterized completely, while the general multi-input case has remained open. In this work, we give a complete characterization for the general multi-input case. In particular, we prove that in addition to accessibility, a necessary and sufficient condition for structural averaged controllability of ensemble systems is existence of a row-saturating matching for its \emph{core}, an acyclic subgraph associated with the system which plays a central role in the result for the single-input case.
