On Computing Stable Lagrangian Subspaces of Hamiltonian Matrices and Symplectic Pencils
On Computing Stable Lagrangian Subspaces of Hamiltonian Matrices and Symplectic Pencils
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 $H^{\infty}$-optimal control, linear-quadratic control and filtering theory, etc. The main approach of our algorithms is to …