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Consistent Initialization and Perturbation Analysis for Abstract Differential-Algebraic Equations

Please always quote using this URN:urn:nbn:de:0296-matheon-3351
  • In this paper we consider linear and time-invariant differential-algebraic equations (DAEs) $E\dot{x}(t)=Ax(t)+f(t)$, $x(0)=x_0$, where $x(\cdot)$ and $f(\cdot)$ are functions with values in separable Hilbert spaces $X$ and $Z$. $E:X\To Z$ is assumed to be a bounded operator, whereas $A$ is closed and defined on some dense subspace $D(A)$ which is in general a proper subset of $X$. Based on a decoupling of the algebraic and the differential part, the set of initial values being consistent with the given inhomogeneity will be parameterized. As a consequence of these results, we will derive estimates for the trajectory $x(\cdot)$ in dependence of the initial state $x_0$ and the inhomogeneity $f(\cdot)$. In the theory of differential-algebraic equations, this is commonly known as perturbation analysis.

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Metadaten
Author:Timo Reis
URN:urn:nbn:de:0296-matheon-3351
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2006/05/18
Release Date:2006/05/18
Tag:
Institute:Technische Universität Berlin
MSC-Classification:34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Axx General theory / 34A09 Implicit equations, differential-algebraic equations [See also 65L80]
34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Gxx Differential equations in abstract spaces [See also 34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx, 58D25] / 34G10 Linear equations [See also 47D06, 47D09]
47-XX OPERATOR THEORY / 47Nxx Miscellaneous applications of operator theory [See also 46Nxx] / 47N70 Applications in systems theory, circuits, and control theory
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Cxx Control systems / 93C05 Linear systems
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Cxx Control systems / 93C25 Systems in abstract spaces
Preprint Number:328
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