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Open AccessJournal ArticleDOI

Solvability conditions, consistency, and weak consistency for linear differential-algebraic equations and time-invariant singular systems: the general case

Ton Geerts
- 01 Mar 1993 - 
- Vol. 181, pp 111-130
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TLDR
In this paper, the authors present several solvability concepts for linear differential-algebraic equations (DAEs) with constant coefficients on the positive time axis as well as for the associated singular systems, and investigate under which conditions these concepts are met.
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This article is published in Linear Algebra and its Applications.The article was published on 1993-03-01 and is currently open access. It has received 99 citations till now. The article focuses on the topics: Weak consistency & Local consistency.

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Citations
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Journal ArticleDOI

Observer design for descriptor systems

TL;DR: Two detectability notions are introduced for the most general class of linear descriptor systems and a unified procedure is provided for the design of observers in both forms.
Journal ArticleDOI

Impulse controllability and observability of rectangular descriptor systems

TL;DR: It is shown that the equivalence between impulse controllability (observability) and the existence of an impulse eliminating semistate feedback (output injection) gain, although true for square descriptor systems, does not hold for rectangular descriptor systems in general.
Book ChapterDOI

Controllability of Linear Differential-Algebraic Systems—A Survey

TL;DR: In this article, different concepts related to controllability of differential-algebraic equations are described and defined in the time domain and equivalent criteria that generalize the Hautus test are presented and proved.
Journal ArticleDOI

Feedback design for regularizing descriptor systems

TL;DR: In this paper, numerical techniques for the regularization of descriptor (generalized state-space) systems by proportional and derivative feedback are surveyed, along with definitions of regularity and index in terms of the Weierstras canonical form.
References
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Book

The Theory of Matrices

TL;DR: In this article, the Routh-Hurwitz problem of singular pencils of matrices has been studied in the context of systems of linear differential equations with variable coefficients, and its applications to the analysis of complex matrices have been discussed.
Book

Théorie des distributions

TL;DR: The merite as discussed by the authors is a date marque une date dans le progres des mathematiques and de la physique en levant l'ambiguite que constituait le succes des methodes de calcul symbolique aupres des physiciens and l'inacceptabilite de leurs formules au regard de la rigueur mathematiques.
Journal ArticleDOI

A generalized state-space for singular systems

TL;DR: In this article, a generalized definition of system order that incorporates these impulsive degrees of freedom is proposed, and concepts of controllability and observability are defined for the impulsive modes.
Journal ArticleDOI

Controllability, observability, and duality in singular systems

TL;DR: In this paper, the concepts of controllability and observability for systems of the form E\dot{x} = Ax + Bu, y = Cx, E singular are considered.
Journal ArticleDOI

Descriptor variable systems and optimal state regulation

TL;DR: In this article, the authors considered linear systems of the form E\dot{x} = Ax + Bu with E singular and proved that the optimal control can be found by solving a reduced order Riccati equation.