Frequency compensation for a class of DAE's arising in electrical circuits

Hennig, Eckhard; Krauße, Dominik; Schafer, Eric L.; Sommer, Ralf; Trunk, Carsten; Winkler, Henrik

doi:10.1002/pamm.201110407

Cited by 2 publications

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“…Hence ( 17) is proved and applying the same estimates for λ ∈ C \ σ(A) proves (18). We continue with the proof of (19). Relation (20) implies…”

Section: Change Of the Root Subspaces Under Rank One Perturbationsmentioning

confidence: 58%

“…From the inequality (19) we see that the number of changeable eigenvalues under a rank one perturbation is bounded by M (A).…”

Section: Change Of the Root Subspaces Under Rank One Perturbationsmentioning

confidence: 99%

“…The aim is to improve the frequency behavior by adding additional capacitances between certain nodes. This corresponds, within the model, to a (structured) rank one perturbation of the matrix E, see [4,7,19]. Here we follow a more general approach and obtain the following results:…”

Section: Introductionmentioning

confidence: 95%

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Eigenvalue Placement for Regular Matrix Pencils with Rank One Perturbations

Gernandt¹,

Trunk²

2017

SIAM J. Matrix Anal. & Appl.

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A regular matrix pencil sE − A and its rank one perturbations are considered. We determine the sets in C ∪ {∞} which are the eigenvalues of the perturbed pencil. We show that the largest Jordan chains at each eigenvalue of sE − A may disappear and the sum of the length of all destroyed Jordan chains is the number of eigenvalues (counted with multiplicities) which can be placed arbitrarily in C ∪ {∞}. We prove sharp upper and lower bounds of the change of the algebraic and geometric multiplicity of an eigenvalue under rank one perturbations. Finally we apply our results to a pole placement problem for a single-input differential algebraic equation with feedback.Keywords: regular matrix pencils, rank one perturbations, spectral perturbation theory MSC 2010: 15A22, 15A18, 47A55 S(sE − A)T = s I r 0 0 N − J 0 0 I n−r , r ∈ {0, 1, . . . , n}

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“…Hence ( 17) is proved and applying the same estimates for λ ∈ C \ σ(A) proves (18). We continue with the proof of (19). Relation (20) implies…”

Section: Change Of the Root Subspaces Under Rank One Perturbationsmentioning

confidence: 58%

“…From the inequality (19) we see that the number of changeable eigenvalues under a rank one perturbation is bounded by M (A).…”

Section: Change Of the Root Subspaces Under Rank One Perturbationsmentioning

confidence: 99%