M.M. Konstantinov; V. Mehrmann; P. Hr. Petkov : Pertubation Analysis for the Hamiltonian Schur Form

Author(s) :

M.M. Konstantinov; V. Mehrmann; P. Hr. Petkov

Title :

Pertubation Analysis for the Hamiltonian Schur Form

Preprint series

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 98-17, 1998

Mathematics Subject Classification :

15A21 [ Canonical forms, etc. ]

93B35 [ Sensitivity (robustness) of control systems ]

93C73 [ Perturbations in control systems ]

Abstract :

In this paper we present a complete perturbation analysis for the Hamiltonian Schur form of a Hamiltonian matrix under similarity transformations widht unitary symplectic matrices. Both local linear and non-linear , non-linear perturbation bounds are presented. The same analysis is also carried out for a less condensed, block-triangular form, and it is shown that this form is less sensitive to perturbations. The analysis is based on the technique of splitting operators and on a representation of the symplectic unitary group which is convenient for perturbation analysis of condensed forms. Given a perturbation in the initial Hamilttonian matrix, the perturbation in the Hamiltonian Schur form and the unitary symplectic basis is constructed in the form of power series expansions. As a corollary a perturbation bound for the stable invariant subspace is obtained.

Keywords :

Hamiltonian Schur form, Riccati equation, unitary symplectic group, perturbation analysis, splitting operators

Language :

english

Publication time :

7/1998

Notes :

supported by grant 5/72 764 of VW Stiftung