Title: On computing stable Lagrangian subspaces of Hamiltonian matrices and symplectic pencils
Authors: Lin, WW
Wang, CS
應用數學系
Department of Applied Mathematics
Keywords: stable Lagrangian subspace;purely imaginary eigenvalue;Hamiltonian matrix;unimodular eigenvalue;symplectic pencil
Issue Date: 1-Jul-1997
Abstract: This paper presents algorithms far computing stable Lagrangian invariant subspaces of a Hamiltonian matrix and a symplectic pencil, respectively, having purely imaginary and unimodular eigenvalues. The problems often arise in solving continuous- or discrete-time H-infinity-optimal control, linear-quadratic control and filtering theory, etc. The main approach of our algorithms is to determine an isotropic Jordan subbasis corresponding to purely imaginary (unimodular) eigenvalues by using the associated Jordan basis of the square of the Hamiltonian matrix (the S + S-1-transformation of. the symplectic pencil). The algorithms preserve structures and are numerically efficient and reliable in that they employ only orthogonal transformations in the continuous case.
URI: http://hdl.handle.net/11536/466
ISSN: 0895-4798
Journal: SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
Volume: 18
Issue: 3
Begin Page: 590
End Page: 614
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  1. A1997XG75900005.pdf