18 documents found

Article / Chapter
All rights reserved
2012-07-04

Addition to : The quasi-Kronecker form for matrix pencils

We refine a result concerning singular matrix pencils and the Wong sequences. In our recent paper (2) we have shown that the Wong sequences are sufficient to obtain a quasi-Kronecker form. However, we applied the Wong sequences again on the regular part to decouple the regular matrix pencil corresponding...
Article / Chapter
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2011-03-04

The quasi-Kronecker form for matrix pencils

We study singular matrix pencils and show that the so called Wong sequences yield a quasi-Kronecker form. This form decouples the matrix pencil into an underdetermined part, a regular part and an overdetermined part. This decoupling is sufficient to fully characterize the solution behaviour of the differential-algebraic...
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...
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...
Article / Chapter
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2009-07-27

The Quasi-Weierstraß form for regular matrix pencils

Dedicated to Heinrich Voß on the occasion of his 65th birthday
Article / Chapter
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2009-03-11

On stability of linear switched differential algebraic equations

This paper studies linear switched differential algebraic equations (DAEs), i.e., systems defined by a finite family of linear DAE subsystems and a switching signal that governs the switching between them. We show by examples that switching between stable subsystems may lead to instability, and that...
Article / Chapter
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2009-02-05

Impulse free solutions for switched differential algebraic equations

Linear switched di erential algebraic equations (switched DAEs) are studied. First, a suitable solution space is introduced, the space of so called piecewisesmooth distributions. Secondly, sufficient conditions are given which ensure that all solutions of the switched DAE are impulse and/or jump free....
Article / Chapter
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2008-11-24

Regularity of distributional differential algebraic equations

Differential algebraic equations (DAEs) of the form Ex = Ax + f are considered. The solutions x and the inhomogeneities f are assumed to be distributions (generalized functions). As a new approach, distributional entries in the coefficient matrices E and A are allowed, in particular, this encompasses...
Article / Chapter
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2008-05-13

Distributional solution theory for linear DAEs

A solution theory for switched linear differential-algebraic equations (DAEs) is developed. To allow for non-smooth coordinate transformation, the coefficients matrices may have distributional entries. Since also distributional solutions are considered it is necessary to define a suitable multiplication...
Article / Chapter
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2008-01-11

A normal form for pure differential algebraic systems

In this paper linear time-invariant differential algebraic equations (DAEs) are studied; the focus is on pure DAEs which are DAEs without an ordinary differential equation (ODE) part. A normal form for pure DAEs is given which is similar to the Byrnes-Isidori normal form for ODEs. Furthermore, the normal...
Article / Chapter
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2007-12-18

Multilayer perceptrons : approximation order and necessary number of hidden un ...

This paper considers the approximation of sufficiently smooth multivariable functions with a multilayer perceptron (MLP). For a given approximation order explicit formulas for the necessary number of hidden units and its distributions to the hidden layers of the MLP is derived. These formulas depend...
Article / Chapter
2006-10-18

Pneumatic cylinders : modelling and feedback force-control

In this paper, we model, analyse, and control an experimental set-up of a servo pneumatic cylinder. The dynamic behaviour of pneumatic actuator systems is dominant by non-linear functions. First, a mathematical model for the pneumatic system is derived. Secondly, we investigate the mathematical properties...
Article / Chapter
2006-03-21

l p Gain Bounds for Switched Adaptive Controllers

A class of discrete plants controlled by a switching adaptive strategy is considered, and lpbounds, 1 ≤ p ≤ ∞, are obtained for the closed loop gain relating input and output disturbances to internal signals.