SIAM Journal on Control and Optimization, Volume 59, Issue 1, Page 417-433, January 2021.
As is well known, the duality mapping on classical linear systems, which is defined by a mere transposition of matrices, makes the concepts of controllability and observability dual to each other. This classical duality theorem, due to Kalman, is extended to a certain important class of multidimensional linear systems.

中文翻译：

---

具有同维数的多维线性系统的对偶$ \ leq 1 $

SIAM控制与优化杂志，第59卷，第1期，第417-433页，2021年1月。
众所周知，经典线性系统上的对偶映射由仅矩阵的转置定义，从而形成了可控性和可控性的概念。可观察性彼此成对。归因于卡尔曼，该经典对偶定理被扩展到一类重要的多维线性系统。