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...
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...
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...
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...
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...
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....
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...
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...
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...
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...
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...
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.