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Prof. Dr. Michael Stiebitz

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Publications at the institute since 1990

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Hotz, Thomas;
Extrinsic vs intrinsic means on the circle. - In: Geometric science of information : first international conference, GSI 2013, Paris, France, August 28 - 30, 2013 ; proceedings.. - Berlin [u.a.] : Springer, ISBN 978-3-642-40020-9, (2013), S. 433-440
Fleischner, Herbert; Stiebitz, Michael
Some remarks on the cycle plus triangles problem. - In: New York [u.a.] : Springer, ISBN 978-1-4614-7253-7, (2013), S. 119-125

Behrndt, Jussi; Leben, Leslie; Martínez Pería, Francisco; Möws, Roland; Trunk, Carsten
Sharp eigenvalue estimates for rank one perturbations of nonnegative operators in Krein spaces. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2013. - Online-Ressource (PDF-Datei: 32 S., 308 KB). . - (Preprint. - M13,13)

Let A and B be selfadjoint operators in a Krein space and assume that the resolvent difference of A and B is of rank one. In the case that A is nonnegative and I is an open interval such that the spectrum of A in I consists of isolated eigenvalues we prove sharp estimates on the numbers and multiplicities of eigenvalues of B in I. The general result is illustrated with eigenvalue estimates for singular left definite Sturm-Liouville differential operators.
Trunk, Carsten;
Locally definitizable operators: the local structure of the spectrum. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2013. - Online-Ressource (PDF-Datei: 16 S., 231 KB). . - (Preprint. - M13,12)

We consider different types of spectral points of locally definitizable operators which can be defined with the help of approximate eigensequences. Their behavior allow a characterization in terms of the (local) spectral function. Moreover, we review some perturbation results for locally definitizable operators.
Anderson, Brian D. O.; Ilchmann, Achim; Wirth, Fabian R.
Stabilizability of linear time-varying systems. - In: Systems & control letters. - Amsterdam [u.a.] : Elsevier, ISSN 1872-7956, Bd. 62 (2013), 9, S. 747-755
Behrndt, Jussi; Philipp, Friedrich; Trunk, Carsten
Bounds on the non-real spectrum of differential operators with indefinite weights. - In: Mathematische Annalen. - Berlin : Springer, ISSN 1432-1807, Bd. 357 (2013), 1, S. 185-213
Berger, Thomas; Ilchmann, Achim; Wirth, Fabian R.
Zero dynamics and stabilization for analytic linear systems. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2013. - Online-Ressource (PDF-Datei: 35 S., 396 KB). . - (Preprint. - M13,11)

The feedback stabilization problem is studied for time-varying real analytic systems. We investigate structural properties of the zero dynamics in terms of a system operator over a skew polynomial ring. The concept of (A,B)-invariant time-varying subspaces included in the kernel of C is used to obtain a condition for stabilizability. This condition is equivalent to autonomy of the zero dynamics in case of time-invariant systems. We derive a zero dynamics form for systems which satisfy an assumption close to autonomous zero dynamics; this in some sense resembles the Byrnes-Isidori form for systems with strict relative degree. Some aspects of the latter are also proved. Finally, we show for square systems with autonomous zero dynamics that there exists a linear state feedback such that the Lyapunov exponent of the closed-loop system equals the Lyapunov exponent of the zero dynamics; some boundedness conditions are required, too. If the zero dynamics are exponentially stable this implies that the system can be exponentially stabilized. These results are to some extent also new for time-invariant systems.
Klöppel, Michaell; Gabash, Aouss; Geletu, Abebe; Li, Pu
Chance constrained optimal power flow with non-Gaussian distributed uncertain wind power generation. - In: 2013 12th International Conference on Environment and Electrical Engineering (EEEIC) : 5 - 8 May 2013, Wroclaw, Poland.. - Piscataway, NJ : IEEE, ISBN 978-1-4673-3060-2, (2013), S. 265-270
Dickinson, Peter J. C.; Eichfelder, Gabriele; Povh, Janez
Erratum to: On the set-semidefinite representation of nonconvex quadratic programs over arbitrary feasible sets. - In: Optimization letters. - Berlin : Springer, ISSN 1862-4480, Bd. 7 (2013), 6, S. 1387-1397

In this paper, an erratum is provided to the article "On the set-semidefinite representation of nonconvex quadratic programs over arbitrary feasible sets", published in Optim Lett, 2012. Due to precise observation of the first author, it has been found that the proof of Lemma 9 has a nontrivial gap, and consequently the main result (Theorem 10) is incorrect. In this erratum, we prove that Corollary 14 is still correct in the original setting while to fix the proof of Theorem 10 we need additional assumptions. We provide a list of different commonly used assumptions making this theorem to be true, and a new version of this theorem, which is now Theorem 17.
Eichfelder, Gabriele; Povh, Janez
On the set-semidefinite representation of nonconvex quadratic programs over arbitrary feasible sets. - In: Optimization letters. - Berlin : Springer, ISSN 1862-4480, Bd. 7 (2013), 6, S. 1373-1386

In the paper we prove that any nonconvex quadratic problem over some set K R^n with additional linear and binary constraints can be rewritten as a linear problem over the cone, dual to the cone of K-semidefinite matrices. We show that when K is defined by one quadratic constraint or by one concave quadratic constraint and one linear inequality, then the resulting K-semidefinite problem is actually a semidefinite programming problem. This generalizes results obtained by Sturm and Zhang (Math Oper Res 28:246-267, 2003). Our result also generalizes thewell-known completely positive representation result from Burer (Math Program 120:479-495, 2009), which is actually a special instance of our result with K = R^n_+.