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