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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
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##### References:
 [1] DOYLE J. C., I.E.E.E. Trans. autom. Control 26 pp 4– (1981) · Zbl 0462.93027 [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 [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
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