Author(s) :
Tatjana Stykel
Preprint series :
Preprint SFB393/ 99-17, Fakultät für Mathematik, TU Chemnitz, D-09107 Chemnitz, Germany, August, 1999.
MSC 2000
- 34D20 Lyapunov stability
-
65F15 Eigenvalues, eigenvectors
Abstract :
This paper discusses Lyapunov stability of the trivial solution of linear
differential-algebraic equations. As a criterion for the asymptotic
stability we propose a numerical parameter $\mbox{\sl\ae}(A,B)$ characterizing
the property of a regular matrix pencil $\lambda A - B$ to have all finite
eigenvalues in the open left half-plane. Numerical aspects for computing this
parameter are discussed.
Keywords :
differential-algebraic equations, asymptotic stability, Lyapunov equation, matrix pencils, deflating subspaces, projections