On computing stable Lagrangian subspaces of Hamiltonian matrices and symplectic pencils

Wen-Wei Lin*, Chern Shuh Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

This paper presents algorithms for 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-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.

Original languageEnglish
Pages (from-to)590-614
Number of pages25
JournalSIAM Journal on Matrix Analysis and Applications
Volume18
Issue number3
DOIs
StatePublished - 1 Jan 1997

Keywords

  • Hamiltonian matrix
  • Purely imaginary eigenvalue
  • Stable Lagrangian subspace
  • Symplectic pencil
  • Unimodular eigenvalue

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