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Tracking through singularities using sliding mode differentiators

Bernardino Castillo-Toledo, Stefano Di Gennaro, Armando López-Cuevas (2015)

Kybernetika

In this work, an alternative solution to the tracking problem for a SISO nonlinear dynamical system exhibiting points of singularity is given. An inversion-based controller is synthesized using the Fliess generalized observability canonical form associated to the system. This form depends on the input and its derivatives. For this purpose, a robust exact differentiator is used for estimating the control derivatives signals with the aim of defining a control law depending on such control derivative...

Tractability of multivariate problems for weighted spaces of functions

H. Woźniakowski (2006)

Banach Center Publications

We survey recent results on tractability of multivariate problems. We mainly restrict ourselves to linear multivariate problems studied in the worst case setting. Typical examples include multivariate integration and function approximation for weighted spaces of smooth functions.

Transitivity of proximinality and norm attaining functionals

Darapaneni Narayana, T. S. S. R. K. Rao (2006)

Colloquium Mathematicae

We study the question of when the set of norm attaining functionals on a Banach space is a linear space. We show that this property is preserved by factor reflexive proximinal subspaces in R ( 1 ) ˜ spaces and generally by taking quotients by proximinal subspaces. We show, for (ℓ₂) and c₀-direct sums of families of reflexive spaces, the transitivity of proximinality for factor reflexive subspaces. We also investigate the linear structure of the set of norm attaining functionals on hyperplanes of c₀ and...

Trigonometric approximation by Nörlund type means in L p -norm

Bogdan Szal (2009)

Commentationes Mathematicae Universitatis Carolinae

We show that the same degree of approximation as in the theorems proved by L. Leindler [Trigonometric approximation in L p -norm, J. Math. Anal. Appl. 302 (2005), 129–136] and P. Chandra [Trigonometric approximation of functions in L p -norm, J. Math. Anal. Appl. 275 (2002), 13–26] is valid for a more general class of lower triangular matrices. We also prove that these theorems are true under weakened assumptions.

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