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<p>For <i>k</i>-valued (control) networks, two types of (control) invariant subspaces are proposed, namely, the state-invariant and dual-invariant subspaces, which are subspaces of the state space and dual space, respectively. Algorithms are presented to check whether a dual subspace is dual- (control) invariant, and to construct state feedback controls. The bearing space of <i>k</i>-valued (control) networks is introduced. Using the structure of the bearing space, the universal invariant subspace is presented, which is independent of the dynamics of particular networks. Finally, the relation between the state-invariant subspaces and the dual-invariant subspaces 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.</p>

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Invariant and Dual-Invariant Subspaces of k-Valued Networks

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Daizhan Cheng,
  • Hongsheng Qi,
  • Xiao Zhang,
  • Zhengping Ji

摘要

For k-valued (control) networks, two types of (control) invariant subspaces are proposed, namely, the state-invariant and dual-invariant subspaces, which are subspaces of the state space and dual space, respectively. Algorithms are presented to check whether a dual subspace is dual- (control) invariant, and to construct state feedback controls. The bearing space of k-valued (control) networks is introduced. Using the structure of the bearing space, the universal invariant subspace is presented, which is independent of the dynamics of particular networks. Finally, the relation between the state-invariant subspaces and the dual-invariant subspaces 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.