Spectral analysis for linear differential-algebraic equations

Pages: 991 - 1000, Issue Special, September 2011

 Abstract        Full Text (329.8K)              

Vu Hoang Linh - Faculty of Mathematics, Mechanics and Informatics, Vietnam National University, 334, Nguyen Trai Str., Thanh Xuan, Hanoi, Vietnam (email)
Volker Mehrmann - Institut für Mathematik, MA 4-5, Technische Universität Berlin, D-10623 Berlin, Fed. Rep., Germany (email)

Abstract: In this paper, the spectral theory of linear di fferential-algebraic equations (DAEs) is discussed. Lyapunov and Sacker-Sell spectra, which are well known for ordinary diff erential equations (ODEs), are studied for linear DAEs and their adjoint equations. The spectral properties of the DAEs are investigated via the so-called essentially underlying ODEs.

Keywords:  di fferential-algebraic equation, underlying ODE, Lyapunov exponent, Sacker-Sell spectrum, exponential dichotomy.
Mathematics Subject Classification:  Primary: 34D08, 34A09; Secondary: 34D09, 65L80

Received: June 2010;      Revised: February 2011;      Published: October 2011.