Solvability conditions, consistency, and weak consistency for linear differential-algebraic equations and time-invariant singular systems: the general case
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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.About:
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.read more
Citations
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Journal ArticleDOI
Theoretical and numerical analysis of differential-algebraic equations
Journal ArticleDOI
Observer design for descriptor systems
M. Hou,P.C. Muller +1 more
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
Joao Y. Ishihara,Marco H. Terra +1 more
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
Thomas Berger,Timo Reis +1 more
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
Angelika Bunse-Gerstner,Ralph Byers,Ralph Byers,Volker Mehrmann,Volker Mehrmann,Volker Mehrmann,Nancy Nichols,Nancy Nichols +7 more
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.
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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.
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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.
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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.