A generalized state-space approach for the additive decomposition of a transfer matrix
Bo Kågström, Paul Van Dooren · 1992
Robust and reliable algorithms are presented for computing the stable projection with respect to a specified region \\Gamma in the complex plane of a transfer matrix given by its generalized state space realization. The algorithms are based on a block-diagonalization of E \\Gamma A (in generalized Schur form) with optimally conditioned transformation matrices. A first direct elimination approach reduces to solving a generalized Sylvester equation. In a second approach an equivalence transformation is constructed from unitary bases of pairs of deflating subspaces obtained from two reorderings of the eigenvalues. The sensitivity of the problem and the stability of the proposed algorithms are discussed and compared with a more classical approach. Results from numerical experiments that evaluate the algorithms and confirm the theory are also reported. Keywords: Transfer matrix, additive decomposition, generalized state space realization, generalized Sylvester equation, block-dia...