Null Controllability of Linear Systems with Constrained Controls

Schmitendorf, W. E.; Barmish, B. Ross

doi:10.1137/0318025

Cited by 162 publications

(48 citation statements)

References 13 publications

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“…Die Arbeiten [23,165,177] zeigen, dass sich der Zustand einer linearen, steuer-und beobachtbaren Strecke (3.1) nur dann von beliebigen Anfangswerten x (0) s ∈ R n s mit einer beschränkten Stellgröße u s ∈ U in die Ruhelage x (R) s = 0 überführen lässt, wenn alle Eigenwerte λ i der Systemmatrix A s einen nichtpositiven Realteil aufweisen, d. h. Re {λ i } ≤ 0 ∀i = 1, . .…”

Section: Stabilisierung Eingangsbeschränkter Systeme: Grenzen Des Mögunclassified

Entwurf von modellbasierten Anti-Windup-Methoden für Systeme mit Stellbegrenzungen

Ortseifen

2014

At – Automatisierungstechnik

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Section: Stabilisierung Eingangsbeschränkter Systeme: Grenzen Des Mögunclassified

Entwurf von modellbasierten Anti-Windup-Methoden für Systeme mit Stellbegrenzungen

Ortseifen

2014

At – Automatisierungstechnik

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“…There is a basic criterion for local null controllability of system (5) which is due to Barmish and Schmitendorf [2,14]. To state it, we introduce the adjoint homogeneous system…”

Section: Digitization and Local Null Controllabilitymentioning

confidence: 99%

Digitization of nonautonomous control systems

Fabbri

Johnson

Kloeden

2005

Journal of Differential Equations

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“…Theorem 3. (Brammer, 1972;Klamka, 1991;Schmitendorf and Barmish, 1980) The dynamic systeṁ (11) and (12) has a positive real part.…”

Section: Approximate Controllability Without Delays With Nonnegative mentioning

confidence: 99%

“…For this purpose, we use Theorem 3, which is well known in the literature (Klamka, 1991;Brammer, 1972;Schmitendorf and Barmish, 1980). While examining the fourth condition of this theorem, we apply the inverse of the Vandermonde matrix.…”

Section: Introductionmentioning

confidence: 99%

Approximate Controllability of Infinite Dimensional Systems of the n-th Order

Respondek¹

2008

International Journal of Applied Mathematics and Computer Science

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The objective of the article is to obtain general conditions for several types of controllability at once for an abstract differential equation of arbitrary order, instead of conditions for a fixed order equation. This innovative approach was possible owing to analyzing the n-th order linear system in the Frobenius form which generates a Jordan transition matrix of the Vandermonde form. We extensively used the fact that the knowledge of the inverse of a Jordan transition matrix enables us to directly verify the controllability by Chen's theorem. We used the explicit analytical form of the inverse Vandermonde matrix. This enabled us to obtain more general conditions for different types of controllability for infinite dimensional systems than the conditions existing in the literature so far. The methods introduced can be easily adapted to the analysis of other dynamic properties of the systems considered.

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Null Controllability of Linear Systems with Constrained Controls

Cited by 162 publications

References 13 publications

Entwurf von modellbasierten Anti-Windup-Methoden für Systeme mit Stellbegrenzungen

Entwurf von modellbasierten Anti-Windup-Methoden für Systeme mit Stellbegrenzungen

Digitization of nonautonomous control systems

Approximate Controllability of Infinite Dimensional Systems of the n-th Order

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