×

On eigenvalues, eigenvectors and singular values in robust stability analysis. (English) Zbl 0551.93056

Recent papers have examined the problem of robustness of the stability of multivariable feedback systems to perturbations \(\Delta\) G in matrix form. Attention has been primarily focused on the use of the maximal singular value \({\bar \sigma}\)(\(\Delta\) G). This paper considers how structured information on the uncertainty in each element \(\Delta_{ij}(s)\) can be used in a similar way based on eigenvalue and singular value analysis.
Reviewer: V.Krakhatko

MSC:

93D25 Input-output approaches in control theory
15A18 Eigenvalues, singular values, and eigenvectors
93B35 Sensitivity (robustness)
93C05 Linear systems in control theory
93C35 Multivariable systems, multidimensional control systems
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] DOYLE J. C., I.E.E.E. Trans. autom. Control 26 pp 4– (1981) · Zbl 0462.93027 · doi:10.1109/TAC.1981.1102555
[2] HALMOS P. R., Finite-dimensional Vector Spaces (1958) · Zbl 0107.01404
[3] KANTOR J. C., I.E.E.E. Trans. autom. Control 28 pp 107– (1983) · Zbl 0502.93056 · doi:10.1109/TAC.1983.1103135
[4] MACFARLANE A. G. J., Complex Variable Methods for Linear MultivariabU Feedback Systems (1980)
[5] OWENS D. H., Feedback and Multivariate Systems (1978) · Zbl 0446.93001
[6] OWENS D. H., Proc. Instn. elect. Engrs 130 pp 45– (1983)
[7] POSTLETHWAITE J., I.E.E.E. Trans. autom. Control 26 pp 32– (1981) · Zbl 0462.93019 · doi:10.1109/TAC.1981.1102556
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.