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M. Konstantinov; V.Mehrmann; P. Petkov : On Properties of General Sylvester and Lyapunov Operators

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
Electronic source:
application/pdf
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 ]
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

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