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

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

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