Estimating Eigenvalues for a class of Dynamic systems

In a previous work an approach was presented for extracting information about the eigenvalues of a linear, time-invariant dynamic system directly from a graphical model. In this paper a generalization is given of the results previously obtained. For some particular cases we can give the entire spectrum. For these cases the spectrum is shown as a function of the structure of an abstract form of the bond graph model. For more general cases, we give upper limits on the imaginery part, and upper and lower limits on the real parts, of the eigenvalues. In contrast to most existing methods, the information about the eigenvalues is generated prior to deriving the state equations. When suitably automated, the results obtained here can provide a considerable reduction in the computational effort required to get information about eigenvalues. This feature is particularly useful in an interactive design context.