Eigenvalue spectra and bounds for certain classes of dynamic systems having tree bond graphs

For a class of linear, time-invariant dynamic systems, information about the eigenvalues of the system can be obtained directly from a graphical model of the system, namely the bond graph model. In contrast to the standard approach, which starts from the state matrix of the system, we use a canonica...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems 1986-12, Vol.33 (12), p.1232-1240
Main Authors: Zeid, A., Rosenberg, R.
Format: Article
Language:English
Subjects:
Bonding
Eigenvalues and eigenfunctions
Equations
Flow graphs
Graph theory
Graphical models
Mechanical engineering
State estimation
Topology
Tree graphs
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Summary:For a class of linear, time-invariant dynamic systems, information about the eigenvalues of the system can be obtained directly from a graphical model of the system, namely the bond graph model. In contrast to the standard approach, which starts from the state matrix of the system, we use a canonical form of the bond graph, namely the gyrobondgraph, to estimate bounds on the eigenvalues of the associated system. For some special cases, the entire spectrum of the system can be obtained by comparing the graph structure to existing graphs with known spectra. For more general cases, bounds are obtained on the largest real and imaginary parts of the eigenvalues as functions of the system's gyrobondgraph topology and its parameters. For some classes of systems, we present a simple graph-based recurrence formula for deriving the characteristic polynomial of a system from a simplified form of its gyrobondgraph. These results, when suitably automated, can reduce the time required to estimate the system performance.
ISSN:0098-4094
1558-1276
DOI:10.1109/TCS.1986.1085879