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Prof. Dr. Achim Ilchmann

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Gernandt, Hannes; Krauße, Dominik; Sommer, Ralf; Trunk, Carsten;
A new method for network redesign via rank one updates - Ilmenau : Technische Universität, Institut für Mathematik, 2017 - 1 Online-Ressource (5 Seiten). . - (Preprint. - M17,08)

We present a method to place the eigenvalues of an electrical network towards a prescribed set of complex numbers by inserting an additional capacitance into the network. We use recent results on rank one perturbations of regular matrix pencils and provide an upper bound on the approximation error of the eigenvalues in the chordal distance.



https://www.db-thueringen.de/receive/dbt_mods_00032770
Worthmann, Karl; Mehrez, Mohamed W.; Mann, George K. I.; Gosine, Raymond G.; Pannek, Jürgen;
Interaction of open and closed loop control in MPC. - In: Automatica : a journal of IFAC, the International Federation of Automatic Control. - Amsterdam [u.a.] : Elsevier, Pergamon Press, ISSN 0005-1098, Bd. 82 (2017), S. 243-250

https://doi.org/10.1016/j.automatica.2017.04.038
Müller, Matthias A.; Worthmann, Karl;
Quadratic costs do not always work in MPC. - In: Automatica : a journal of IFAC, the International Federation of Automatic Control. - Amsterdam [u.a.] : Elsevier, Pergamon Press, ISSN 0005-1098, Bd. 82 (2017), S. 269-277

https://doi.org/10.1016/j.automatica.2017.04.058
Fleige, Andreas; Winkler, Henrik;
An indefinite inverse spectral problem of Stieltjes type. - In: Integral equations and operator theory : IEOT. - Berlin : Springer, ISSN 1420-8989, Bd. 87 (2017), 4, S. 491-514

https://doi.org/10.1007/s00020-017-2358-x
Gernandt, Hannes; Trunk, Carsten;
Eigenvalue placement for regular matrix pencils with rank one perturbations. - In: SIAM journal on matrix analysis and applications - Philadelphia, Pa. : Soc., ISSN 1095-7162, Bd. 38 (2017), 1, S. 134-154

http://dx.doi.org/10.1137/16M1066877
Ilchmann, Achim; Reis, Timo
. - Surveys in differential-algebraic equations ; 4 - Cham : Springer, 2017 - ix, 305 Seiten. . - (Differential-algebraic equations forum)
Jacob, Birgit; Tretter, Christiane; Trunk, Carsten; Vogt, Hendrik;
Numerical range and quadratic numerical range for damped systems - Ilmenau : Technische Universität, Institut für Mathematik, 2017 - 1 Online-Ressource (27 Seiten). . - (Preprint. - M17,05)

We prove new enclosures for the spectrum of non-selfadjoint operator matrices associated with second order linear differential equations z'' (t) + D z' (t) + A_0 z(t) = 0 in a Hilbert space. Our main tool is the quadratic numerical range for which we establish the spectral inclusion property under weak assumptions on the operators involved; in particular, the damping operator only needs to be accretive and may have the same strength as A_0. By means of the quadratic numerical range, we establish tight spectral estimates in terms of the unbounded operator coefficients A_0 and D which improve earlier results for sectorial and selfadjoint D; in contrast to numerical range bounds, our enclosures may even provide bounded imaginary part of the spectrum or a spectral free vertical strip. An application to small transverse oscillations of a horizontal pipe carrying a steady-state flow of an ideal incompressible fluid illustrates that our new bounds are explicit.



https://www.db-thueringen.de/receive/dbt_mods_00031984
Ilchmann, Achim; Reis, Timo;
Outer transfer functions of differential-algebraic systems. - In: Control, optimisation and calculus of variations : COCV. - Les Ulis : EDP Sciences, ISSN 1262-3377, Bd. 23 (2017), 2, S. 391-425

https://doi.org/10.1051/cocv/2015051
Derkach, Vladimir; Trunk, Carsten;
Coupling of definitizable operators in Krein spaces - Ilmenau : Technische Universität, Institut für Mathematik, 2017 - 1 Online-Ressource (18 Seiten). . - (Preprint. - M17,03)

Indefinite Sturm-Liouville operators defined on the real line are often considered as a coupling of two semibounded symmetric operators defined on the positive and the negative half axis. In many situations, those two semibounded symmetric operators have in a special sense good properties like a Hilbert space self-adjoint extension. In this paper we present an abstract approach to the coupling of two (definitizable) self-adjoint operators. We obtain a characterization for the definitizability and the regularity of the critical points. Finally we study a typical class of indefinite Sturm-Liouville problems on the real line.



https://www.db-thueringen.de/receive/dbt_mods_00031469
Fleige, Andreas; Winkler, Henrik;
An indefinite inverse spectral problem of Stieltjes type - Ilmenau : Technische Universität, Institut für Mathematik, 2017 - 1 Online-Ressource (25 Seiten). . - (Preprint. - M17,02)
https://www.db-thueringen.de/receive/dbt_mods_00031460