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Constrained Common Invariant Subspace and Its Application
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DOI：10.1109/TAC.2024.3378769.png)
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摘要
En 中文
The notion of constrained common invariant subspaces (CCISs) is proposed in this article as a generalization of the well-known invariant subspace to study the structural properties of multiple matrices. Specifically, some necessary and sufficient conditions for the existence of a CCIS are established to provide a methodology to compute such a CCIS. Then, the properties of CCISs and their relation to common eigenvectors are revealed. The existence of common eigenvectors leads to the existence of CCIS, but not vice versa, so the established CCIS can reveal the structural properties of multiple matrices better than common eigenvectors can. The established CCIS is applied to the reducibility of Fornasini-Marchesini (F-M) state-space models, i.e., the necessary and sufficient conditions and the related algorithm for reducibility of F-M models are developed. Finally, a gain-scheduled state-feedback control is proposed for a rational parameter system to further demonstrate the superiority of the established CCIS.
Keyword:
Vectors
Kernel
Heuristic algorithms
Computational modeling
Time-varying systems
Symbols
State-space methods
Invariant subspace (IS)
order reduction
rational parameter system
state-feedback control
期刊
IF:
7
论文数:
1.3W
被引数:
6.7W
机构
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