Eigenvalue and state-transition sensitivity of linear systems

Nicholson, Helen

doi:10.1049/piee.1967.0376

Cited by 7 publications

(1 citation statement)

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“…The sensitivity of the prediction algorithm based on spectral expansion will require knowledge of the sensitivity of the eigenvalue analysis of the defining covariance data matrix. Various techniques have been developed for relating eigenvalue change to differential matrix element changes [18-221, and the basic role of Sylvester's expansion theorem associated with the spectral decomposition of a matrix and of the constituent matrices in this development have been illustrated [18]. A differential change of dA in the matrix A possessing distinct eigenvalues has been shown to produce the small first-order eigenvalue variation where the eigenvector and eigenrow ur and v, respectively are defined by the relations…”

Section: Sensitivity Of the Spectral Prediction Algorithmmentioning

confidence: 99%

Sequential least-squares prediction based on spectral analysis

Nicholson

1972

International Journal of Computer Mathematics

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A spectral representation for time series analysis is formulated on the basis of classical leastsquares theory, and is extended for application to the prediction of a random sequence with a sequential updating of model coefficients based on pre-computed eigenvector components and current online data. The solution for updating the time series coefficients is shown to be directly analogous to the form of piecewise solution of the steady-state electrical network problem based on Kron's method of tearing and interconnection. The sensitivity of the spectral prediction algorithm based on the eigenvalue properties of the defining covariance data matrix is also developed.

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Section: Sensitivity Of the Spectral Prediction Algorithmmentioning

confidence: 99%

Sequential least-squares prediction based on spectral analysis

Nicholson

1972

International Journal of Computer Mathematics

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Independent Estimation of Generator Clustering and Islanding Conditions in Power System with Microgrid and Inverter-Based Generation

et al. 2020

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Constrained system perturbation analysis

Gibson

Hamilton-Jenkins

1981

International Journal of Systems Science

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Alternative formulations of eigenvalue perturbations for unconstrained paremeter systems with distinct eigenvalues extend simply to constrained systems. Eigenvalue sensitivity matrix rank conditions determine feasibility of parameter augmentations for the inverse problem of eigenvalue placement. An eigenvector matrix perturbation equation yields another view of perturbation theory and yields simple expressions for systcms with ' singular structure ' in which eigenvectora are invariant under perturbation.

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Eigenvalue and state-transition sensitivity of linear systems

Cited by 7 publications

References 8 publications

Sequential least-squares prediction based on spectral analysis

Sequential least-squares prediction based on spectral analysis

Independent Estimation of Generator Clustering and Islanding Conditions in Power System with Microgrid and Inverter-Based Generation

Constrained system perturbation analysis

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