Author(s) :
Michael Karow
,
Diederich Hinrichsen
,
Anthony J. Pritchard
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 09-2005
MSC 2000
- 93D09 Robust stability
-
93B60 Eigenvalue problems
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.
Keywords :
interconnected systems, spectral value sets, stability radii, μ-analysis, robustness