Two-dimensional behavior decompositions with Finite-Dimensional Intersection: A Complete Characterization
Two-dimensional behavior decompositions with Finite-Dimensional Intersection: A Complete Characterization
复制标题
具有有限维交集的二维行为分解：完整的表征
DOI：
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发表时间：
2005
影响因子：
2.5
通讯作者：
M. E. Valcher
中科院分区：
文献类型：
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作者：
M. Bisiacco;M. E. Valcher
摘要本文解决了以下问题：给定一个二维完整行为
$${cal B}$$ 及其子行为之一
$${cal B}_B$$，在什么条件下第三个完整的行为
可以找到$${cal B}_A$$，这样
$${cal B} = {cal B}_A + {cal B}_B$$ 和
$${cal B}_A cap {cal B}_B$$ 是有限维自治的吗？这构成了分解定理的完整推广，因为它表示具有“最小交集”的分解，其中两项之一已先验固定。这里进行的分析完成了 [Bisiacco 和 Valcher，多维系统和信号处理，卷。 13，2002 年，第 289–315 页]。并完全概括了 [Bisiacco 和 Valcher, IEEE Transactions on Circuits and Systems Part I, CAS-I-48, no-4, 2001, pp. 490–494] 中提出的直和分解问题。
AbstractIn this paper, the following problem is addressed: given a two-dimensional complete behavior
$${cal B}$$ and one of its sub-behaviors
$${cal B}_B$$, under what conditions a third complete behavior
$${cal B}_A$$ can be found, such that
$${cal B} = {cal B}_A + {cal B}_B$$ and
$${cal B}_A cap {cal B}_B$$ is finite-dimensional autonomous? This constitutes a complete generalization of the decomposition theorem, as it represents a decomposition with “minimal intersection”, in which one of the two terms has been a priori fixed. The analysis carried on here completes the preliminary results reported in [Bisiacco and Valcher, Multidimensional Systems and Signal Processing, vol. 13,2002, pp. 289–315]. and completely generalizes the direct sum decomposition problem presented in [Bisiacco and Valcher, IEEE Transactions on Circuits and Systems Part I, CAS-I-48, no-4, 2001, pp. 490–494].