This paper deals with strong structural controllability of linear structured systems in which the system matrices are given by zero/nonzero/arbitrary pattern matrices. Instead of assuming that the nonzero and arbitrary entries of the system matrices can take their values completely independently, this paper allows equality constraints on these entries, in the sense that a priori given entries in the system matrices are restricted to take arbitrary but identical values. To formalize this general class of structured systems, we introduce the concepts of colored pattern matrices and colored structured systems. The main contribution of this paper is that it generalizes both the classical results on strong structural controllability of structured systems as well as recent results on controllability of systems defined on colored graphs. In this paper we will establish both algebraic and graph-theoretic conditions for strong structural controllability of this more general class of structured systems.

本文讨论了线性结构系统的强大结构可控性，其中系统矩阵由零/非零/任意模式矩阵给出。代替假设系统矩阵的非零条目和任意条目可以完全独立地获取其值，本文从先验的意义上允许对这些条目进行等式约束系统矩阵中的给定条目被限制为采用任意但相同的值。为了正式化这一类结构化系统的一般形式，我们介绍了彩色图案矩阵和彩色结构化系统的概念。本文的主要贡献在于，它概括了有关结构化系统的强结构可控性的经典结果以及有关彩色图上定义的系统的可控性的最新结果。在本文中，我们将建立代数条件和图论条件，以使这种更通用的结构化系统类具有较强的结构可控性。