Interconnected Systems with Uncertain Couplings: Explicit Formulae for mu-Values, Spectral Value Sets, and Stability Radii

Authors:
Michael Karow;Diederich Hinrichsen;Anthony J. Pritchard
Affiliations:
-;-;-
Venue:
SIAM Journal on Control and Optimization
Year:
2006

Citing 0
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Abstract

In this paper we study the variation of the spectrum of block-diagonal systems under perturbations of compatible block structure with fixed zero blocks at arbitrarily prescribed locations ("Gershgorin-type perturbations"). We derive explicit and computable formulae for the associated mu-values. The results are then applied to characterize spectral value sets and stability radii for such perturbed systems. By specializing our results to the scalar diagonal case, the classical eigenvalue inclusion theorems of Gershgorin, Brauer, and Brualdi are obtained as corollaries. Moreover it follows that the inclusion regions of Brauer and Brualdi are optimal for the corresponding perturbation structures.