On structured realizability and stabilizability of linear systems
On structured realizability and stabilizability of linear systems
复制标题
线性系统的结构化可实现性和稳定性
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
A. Rantzer
中科院分区：
文献类型：
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作者：
Laurent Lessard;Maxim Kristalny;A. Rantzer
我们研究通过图定义的线性系统的结构化可实现性的概念。如果状态空间矩阵继承关联图的邻接矩阵的稀疏模式，则构建可稳定且可检测的实现。在本文中，我们证明并非每个结构化传输矩阵都有结构化实现，并揭示了这一事实的实际意义。我们还揭示了对象的结构化可实现性与对象是否可以通过结构化控制器稳定之间的密切联系。特别是，我们表明，只有当被控对象承认结构化实现时，结构化稳定控制器才能存在。最后，我们给出了所有结构化稳定控制器的参数化，并表明它们总是具有结构化的实现。
We study the notion of structured realizability for linear systems defined over graphs. A stabilizable and detectable realization is structured if the state-space matrices inherit the sparsity pattern of the adjacency matrix of the associated graph. In this paper, we demonstrate that not every structured transfer matrix has a structured realization and we reveal the practical meaning of this fact. We also uncover a close connection between the structured realizability of a plant and whether the plant can be stabilized by a structured controller. In particular, we show that a structured stabilizing controller can only exist when the plant admits a structured realization. Finally, we give a parameterization of all structured stabilizing controllers and show that they always have structured realizations.