A graph-theoretic method to find decentralized fixed modes of LTI systems

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• 作者：Javad Lavaei ; Amir G. Aghdam
• 关键词：Decentralized control ; Stabilizability ; Graph theory
• 刊名：Automatica
• 出版年：2007
• 出版时间：December 2007
• 年：2007
• 卷：43
• 期：12
• 页码：2129-2133
• 全文大小：159 K

文摘

This paper deals with the decentralized pole assignability of interconnected systems by means of linear time-invariant (LTI) controllers. A simple graph-theoretic approach is proposed to identify the distinct decentralized fixed modes (DFMs) of the system, i.e., the unrepeated modes which cannot be moved by means of a LTI decentralized controller. The state-space representation of the system is transformed to the decoupled form using a proper change of coordinates. For any unrepeated mode, a matrix is then computed which resembles the transfer function matrix of the system at some point in the complex plane. A bipartite graph is constructed accordingly in terms of the computed matrix. Now, the problem of verifying if this mode is a DFM of the system reduces to checking if the constructed graph has a complete bipartite subgraph with a certain property. The sole restriction of this work is that it is only capable of identifying the distinct DFMs of a system. However, it is axiomatic that most of the modes of the real-world systems are normally distinct. The primary advantage of the present paper is its simplicity, compared to the existing ones which often require evaluating the rank of several matrices.