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Numerical Linear Algebra Methods for Linear Differential-Algebraic Equations

Please always quote using this URN:urn:nbn:de:0296-matheon-13318
  • A survey of methods from numerical linear algebra for linear constant coefficient differential-algebraic equations (DAEs) and descriptor control systems is presented. We discuss numerical methods to check the solvability properties of DAEs as well as index reduction and regularization techniques. For descriptor systems we discuss controllability and observability properties and how these can be checked numerically. These methods are based on staircase forms and derivative arrays, transformed with real orthogonal transformations that are discussed in detail. Then we use the reformulated problems in several control applications for differential-algebraic equations ranging from regular and singular linear-quadratic optimal and robust control to dissipativity checking. We discuss these applications and give a systematic overview over the theory and the numerical solution methods. In particular, we show that all these applications can be treated with a common approach that is based on the computation of eigenvalues and deflating subspaces of even matrix pencils. The unified approach allows to generalize and improve several techniques that are currently in use in systems and control.

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Metadaten
Author:Peter Benner, Philip Losse, Volker Mehrmann, Matthias Voigt
URN:urn:nbn:de:0296-matheon-13318
Referee:Caren Tischendorf
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2014/12/08
Release Date:2014/12/08
Tag:$\mathcal{H}_\infty$ control; descriptor system; differential-algebraic equation; dissipativity; even matrix pencil; linear-quadratic optimal control
Institute:Technische Universität Berlin
MSC-Classification:34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Axx General theory / 34A09 Implicit equations, differential-algebraic equations [See also 65L80]
65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F15 Eigenvalues, eigenvectors
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Cxx Control systems / 93C05 Linear systems
Preprint Number:1074
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