TU Chemnitz, Fakultät für Mathematik: Fakultät für Mathematik
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M. Konstantinov; V.Mehrmann; P. Petkov : On Properties of General Sylvester and Lyapunov Operators
- Author(s) :
- M. Konstantinov; V.Mehrmann; P. Petkov
- Title :
- On Properties of General Sylvester and Lyapunov Operators
- Preprint series
- Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 98-12, 1998
- Mathematics Subject Classification :
- 15A24 [ Matrix equations
]
- 93B35 [ Sensitivity (robustness) of control systems ]
- 93C73 [ Perturbations in control systems ]
- 93B35 [ Sensitivity (robustness) of control systems ]
- Abstract :
- General Sylvester and Lyapunov operators in real
and complex matrix spaces are studied, which include as a particular case the operators arising in the theory
of linear time-invariant descriptor systems. For linear
matrix operators an index which characterizes the operator
is introduced and determined for general linear matrix
operators. The problem of representing such an
operator as a sum of elementary operators is posed and solved. The dimensions
of the spaces of Lyapunov operators are determined and the concept of symmetrised singular
values of a Lyapunov operator is introduced. The application
of symmetric singular values to the perturbation and error analysis of
Lyapunov equations is discussed.
- Keywords :
- Linear matrix operators, Sylvester operators, Lyapunov operators, singular values, symmetrised singular values, perturbation analysis and error analysis
- Language :
- english
- Publication time :
- 6/1998
- Notes :
- supported by grand 5/72 764 of VW Stiftung
