128 documents found

Book
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2017-09-13

EAGLE-Starthilfe Mathematik und Gesellschaft : zur Funktion der angewandten Ma ...

Was ist Wissenschaft? Einzelwissenschaften. Attribute und Einteilung der Wissenschaften. Mathematik. Entstehung der angewandten Mathematik (1543-1794). Reine und angewandte Mathematik (1794-1860). Anwendung der angewandten Mathematik (1860-1920). Transformation der Naturwissenschaften in Technologie im...
Ilmenau: ilmedia, 2017-09-13
Dissertation
2015-09-01

On Output Feedback Control of Infinite-dimensional Systems

Diese Dissertation behandelt zeitinvariante, unendlichdimensionale, lineare Systeme, die ein Eingangssignal u in ein Ausgangssignal y umwandeln.In der Theorie der kompatiblen, wohlgestellten, linearen Systeme, werden solche Umwandlungen durch Differenzialgleichungen der Formx'(t)=Ax(t)+ Bu(t), y(t)=Cx(t)+Du(t)...
Article / Chapter
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2015-01-29

Zur gesellschaftlichen Funktion der angewandten Mathematik

Der Begriff derWissenschaft wird expliziert; die Einzelwissenschaften Philosophie, Natur und Technikwissenschaften und Mathematik werden historisch und systematisch eingeordnet, um insbesondere den Unterschied zwischen Technologie und angewandter Mathematik zu verstehen. Es wird dann Peter Bulthaups...
Article / Chapter
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2014-10-07

Outer transfer functions of differential-algebraic systems

We consider differential-algebraic systems whose transfer function is outer: i.e., it has full row rank and all transmission zeros lie in the closed left half complex plane. We characterize outer, with the aid of the Kronecker structure of the system pencil and the Smith-McMillan structure of the transfer...
Dissertation
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2013-11-08

On differential-algebraic control systems

In der vorliegenden Dissertation werden differential-algebraische Gleichungen (differential-algebraic equations, DAEs) der Form $\ddt E x = Ax + f$ betrachtet, wobei $E$ und $A$ beliebige Matrizen sind. Falls $E$ nichtverschwindende Einträge hat, dann kommen in der Gleichung Ableitungen der entsprechenden...
Article / Chapter
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2013-10-24

The Byrnes-Isidori form for infinite-dimensional systems

We define a Byrnes-Isidori form for a class of infinite-dimensional systems with relative degree r and show that any system belonging to this class can be transformed into this form. We also analyze the concept of (stable) zero dynamics and show that it is, together with the Byrnes-Isidori form, instrumental...
Article / Chapter
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2013-08-15

Zero dynamics and stabilization for analytic linear systems

The feedback stabilization problem is studied for time-varying real analytic systems. We investigate structural properties of the zero dynamics in terms of a system operator over a skew polynomial ring. The concept of (A,B)-invariant time-varying subspaces included in the kernel of C is used to obtain...
Article / Chapter
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2013-01-18

On minimum phase

Wir diskutieren Minimalphasigkeit von schwach-stabilen Transferfunktionen; letzteres sind rationale Funktionen, bei denen das Nennerpolynom Nullstellen in der abgeschlossenen linken komplexen Halbebene hat. Minimalphasigkeit wird hier mittels der Ableitung der Argumentfunktion der Transferfunktion definiert....
Article / Chapter
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2012-12-19

Stabilization of linear time-varying systems

For linear time-varying systems with bounded system matrices we discuss the problem of stabilizability by linear state feedback. It is shown that an optimal control approach yields a criterion in terms of the cost for stabilizability. The constants appearing in the criterion of optimality allow for the...
Article / Chapter
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2012-06-01

Decentralized tracking of interconnected systems

Decentralized funnel controllers are applied to finitely many interacting single-input single-output, minimum phase, relative degree one systems in order to track reference signals of each system within a prespecified performance funnel. The reference signals as well as the systems belong to a fairly...
Article / Chapter
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2011-07-28

Normal forms, high-gain and funnel control for linear differential-algebraic...

We consider linear differential-algebraic m-input m-output systems with positive strict relative degree or proper inverse transfer function; in the single-input single-output case these two disjoint classes make the whole of all linear DAEs without feedthrough term. Structural properties - such as normal...
Article / Chapter
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2010-11-16

Zero dynamics and funnel control of linear differential-algebraic systems

We study the class of linear differential-algebraic m-input m-output systems which have a transfer function with proper inverse. A sufficient condition for the transfer function to have proper inverse it that the system has 'strict and non-positive relative degree'. We present two main results: First,...
Dissertation
2010-10-27

Feedback control : systems with higher unknown relative degree, input constrai ...

The thesis deals with the control of m-input, m-output systems with unknown but bounded relative degree and Volterra-Stieltjes systems. The two control strategies are: adaptive high-gain output derivative feedback and funnel control. The aim is the development of feedback controllers which achieves output...
Article / Chapter
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2010-10-12

On stability of time-varying linear differential-algebraic equations

We develop a stability theory for time-varying linear differential algebraic equations (DAEs). Standard stability concepts for ODEs are formulated for DAEs and characterized. Lyapunov’s direct method is derived as well as the converse of the stability theorems. Stronger results are achieved for DAEs...
Article / Chapter
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2010-07-23

Time-varying linear DAEs transferable into standard canonical form

We introduce a solution theoryfor time-varying linear differential-algebraic equations(DAEs) E(t)˙x = A(t)x which can be transformed into standard canonical form (SCF), i.e. the DAE is decoupled into an ODE ˙z1 = J(t)z1 and a pure DAE N(t)˙z1 = z1 , where N is pointwise strictly lower triangular. This...
Article / Chapter
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2010-07-05

Funnel control for systems with relative degree two

Tracking of reference signals yref(·) by the output y(·) of linear (as well as a considerably large class of nonlinear) single-input, single-output system is considered. The system is assumed to have strict relative degree two with ("weak") stable zero dynamics. The control objective is tracking of...
Article / Chapter
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2010-06-03

Zero dynamics of time-varying linear systems

The Byrnes-Isidori form with respect to the relative degree is studied for time-varying linear multi-input, multi-output systems. It is clarified in which sense this form is a normal form. (A,B)-invarianttime-varying subspaces are defined and the maximal(A,B)-invariant time-varying subspace included...
Article / Chapter
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2009-09-23

Funnel control with saturation : nonlinear SISO systems

Tracking - by the system output - of a reference signal (assumed bounded with essentially bounded derivative) is considered in the context of a class of nonlinear, single-input, single-output systems modelled by functional differential equations and subject to input saturation. Prespecified is a parameterized...
Dissertation
2009-08-24

Output feedback control and robustness in the gap metric

Zusammenfassung Mueller, Markus: Output feedback control and robustness in the gap metric Ilmenau : Univ.-Verl. Ilmenau, 2009. - 254 S. ISBN 978-3-939473-60-2 Die vorgelegte Arbeit behandelt den Entwurf und die Robustheit von drei verschiedenen Regelstrategien für lineare Differentialgleichungssysteme...
Dissertation
2009-07-31

Distributional differential algebraic equations

Trenn, Stephan:Distributional differential algebraic equations(Zusammenfassung, Diss., Technische Universität Ilmenau, 2009) Lineare implizite Differentialgleichungen der Form Ex'=Ax+f werden untersucht. Da die Matrix E nicht als invertierbar angenommen wird, enthält das Gleichungssystem neben...