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

Title:

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

Lavaei, Javad and Aghdam, Amir G. (2007) A graph-theoretic method to find decentralized fixed modes of LTI systems. Automatica, 43 (12). pp. 2129-2133. ISSN 00051098

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Official URL: http://dx.doi.org/10.1016/j.automatica.2007.04.019

Abstract

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.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Electrical and Computer Engineering
Item Type:Article
Refereed:Yes
Authors:Lavaei, Javad and Aghdam, Amir G.
Journal or Publication:Automatica
Date:2007
Digital Object Identifier (DOI):10.1016/j.automatica.2007.04.019
Keywords:Decentralized control; Stabilizability; Graph theory
ID Code:975163
Deposited By: DANIELLE DENNIE
Deposited On:22 Jan 2013 13:39
Last Modified:18 Jan 2018 17:39

References:

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Lavaei and Aghdam, 2006a Lavaei, J., & Aghdam, A. G. (2006a). Elimination of fixed modes by means of high-performance constrained periodic control. In Proceedings of the 45th IEEE conference on decision and control (pp. 4441–4447). San Diego, CA.

Lavaei and Aghdam, 2006b Lavaei, J., & Aghdam, A. G. (2006b). Decentralized control design for interconnected systems based on a centralized reference controller. In Proceedings of the 45th IEEE conference on decision and control (pp. 1189–1195). San Diego, CA.

Lavaei et al., 2006 Lavaei, J., Momeni, A., & Aghdam, A. G. (2006). Spacecraft formation control in deep space with reduced communication requirement. IEEE Transactions on Control Systems Technology, to appear.

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