Tatyana Shtykel
On the criterion of asymptotical stability for index-1 tractable DAEs
Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976)

MSC:

15A22 Matrix pencils, See also {47A56}

34D20 Lyapunov stability

65F15 Eigenvalues, eigenvectors

Abstract: This paper considers the index-1 tractable differential-algebraic equation. The Lyapunov stability of the trivial solution is discussed. As a criterion of the asymptotical stability we propose a numerical parameter æ(A,B) characterizing the property of the index-1 matrix pencil {A, B} to have all finite eigenvalues within the negative complex half-plane. An algorithm for computing this parameter is described.
Keywords: differential algebraic equation, Lyapunov stability, matrix pencil, projector