Text
Perturbation Theory of Transfer Function Matrices
Zeros of rational transfer function matrices
are the eigenvalues of associated polynomial system matrices
under minimality conditions. In this paper, we define a structured condition number for a simple eigenvalue
of a (locally) minimal polynomial system matrix
, which in turn is a simple zero
of its transfer function matrix
. Since any rational matrix can be written as the transfer function of a polynomial system matrix, our analysis yields a structured perturbation theory for simple zeros of rational matrices
. To capture all the zeros of
, regardless of whether they are poles, we consider the notion of root vectors. As corollaries of the main results, we pay particular attention to the special case of
being not a pole of
since in this case the results get simpler and can be useful in practice. We also compare our structured condition number with Tisseur’s unstructured condition number for eigenvalues of matrix polynomials and show that the latter can be unboundedly larger. Finally, we corroborate our analysis by numerical experiments.
Barcode | Tipe Koleksi | Nomor Panggil | Lokasi | Status | |
---|---|---|---|---|---|
art147319 | null | Artikel | Gdg9-Lt3 | Tersedia namun tidak untuk dipinjamkan - No Loan |
Tidak tersedia versi lain