## Berichte der Arbeitsgruppe Technomathematik (AGTM Report)

68

Elements of the differential topology are used to prove necessary conditions for stabilizability in large by a smooth feedback. Criteria for the smooth feedback stabilizing a smooth nonlinear system locally to have the smooth piecewise smooth extension, which stabilizes the system over a given compact set, have been obtained.

69

A method of decoupling normalizing transformations has been developed. According to the method only the part of differential equations corresponding to the dynamic on a center manifold has to be modified by means of the normalizing transformations of a Poincare type. The existence of the normalizing transformation completely decoupling the stable dynamic from the center manifold dynamic has been proved. A numerical procedure for the calculation of asymptotic series for the decoupling normalizing transformation has been proposed. The developed method is especially important for the perturbation theory of center manifold and, in particular, for the local stabilization theory. In the paper some sufficient conditions for local stabilization have been given.

70

71

72

The performance of napkins is nowadays improved substantially by embedding granules of a superabsorbent into the cellulose matrix. In this paper a continuous model for the liquid transport in such an Ultra Napkin is proposed. Its mean feature is a nonlinear diffusion equation strongly coupled with an ODE describing a reversible absorbtion process. An efficient numerical method based on a symmetrical time splitting and a finite difference scheme of ADI-predictor-corrector type has been developed to solve these equations in a three dimensional setting. Numerical results are presented that can be used to optimize the granule distribution.

74

On the Mróz Model
(1992)

75

In this paper noises and disturbances are treated as distributions of some general class. The problem of sensitivity minimization is considered. A design procedure for the construction of Luenberger observers which estimate the state of a system with a given rate of accuracy has been proposed. The design procedure is applied to identify the first derivatives of an oscillating signal. The constraints on a noise and on a sampling which are necessary to estimate the derivatives to a given accuracy have been obtained.

76

77

A multiparameter, polynomial feedback strategy is introduced to solve the universal adapative tracking problem for a class of multivariable minimum phase system and reference signals generated by a known linear time-invariant differential equation. For 2-input, 2-output, minimum phase systems (A,B,C) with det(CB)0, a different polynomial tracking controller is given which does not invoke a spectrum unmixing set.