Spectral analysis for linear differential-algebraic equations

Vu Hoang Linh; Volker Mehrmann

doi:10.3934/proc.2011.2011.991

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2011, Volume 2011: 991-1000. Doi: 10.3934/proc.2011.2011.991 open access

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Spectral analysis for linear differential-algebraic equations

Vu Hoang Linh^1, and
Volker Mehrmann^2,

1.
Faculty of Mathematics, Mechanics and Informatics, Vietnam National University, 334, Nguyen Trai Str., Thanh Xuan, Hanoi
2.
Institut für Mathematik, MA 4-5, Technische Universität Berlin, D-10623 Berlin, Fed. Rep.

Received: May 31, 2010

Revised: January 31, 2011

Published: August 2017

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Abstract

In this paper, the spectral theory of linear differential-algebraic equations (DAEs) is discussed. Lyapunov and Sacker-Sell spectra, which are well known for ordinary differential 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.

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Mathematics Subject Classification: Primary: 34D08, 34A09; Secondary: 34D09, 65L80.

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