Institut für Allgemeine Elektrotechnik, Uni Rostock - Universität ...

Properties of the System Matrix
Properties of the system matrix:
i All eigenvalues of A lie on the imaginary axis.
λ A ,i
They are either 0 or complex-conjugate in pairs.
i A complete basis of eigenvectors exists.
Eigenvectors of different eigenvalues are orthogonal.
A simple estimate for the absolute largest eigenvalue ω
yields ω
max
≤ A' for any arbitrary matrix norm.
= max λ
max A,i
Example: µ ≡ µ , ε ≡ε
, Δ u = Δ v = Δ w = Δ yields :
0 0
1 ⎛0 −C⎞
4c
A' = ⎜ ⎟ ⇒ A' = A'
=
∞ 1
µ
0ε
Δ
0Δ ⎝C 0 ⎠
0
Prof. Dr. Ursula van Rienen, Universität Rostock, Fakultät für Informatik und Elektrotechnik (IEF), Institut für Allgemeine Elektrotechnik (IAE)
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