论文标题
$ k $值网络的不变和双不变子空间
Invariant and Dual Invariant Subspaces of $k$-valued Networks
论文作者
论文摘要
考虑一个$ k $值的网络。提出了两种（控制）不变子空间，称为状态和双不变子空间，分别是状态空间和双空间的子空间。提出算法以验证双重空间是双重控制不变子空间。引入了$ k $值（控制）网络的轴承空间。使用轴承空间的结构，引入了通用不变子空间，该子空间与特定网络的动力学无关。最后，研究了网络不变子空间与双重不变子空间之间的关系。双重性属性表明，如果双重空间是不变的，那么其垂直状态子空间也是不变的，反之亦然。
Consider a $k$-valued network. Two kinds of (control) invariant subspaces, called state and dual invariant subspaces, are proposed, which are subspaces of state space and dual space respectively. Algorithms are presented to verify whether a dual subspace is a dual or dual control invariant subspace. The bearing space of $k$-valued (control) networks is introduced. Using the structure of bearing space, the universal invariant subspace is introduced, which is independent of the dynamics of particular networks. Finally, the relationship between state invariant subspace and dual invariant subspace of a network is investigated. A duality property shows that if a dual subspace is invariant then its perpendicular state subspace is also invariant and vice versa.
