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Veröffentlichungen am Institut für Mathematik seit 1990

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Berger, Thomas; Trenn, Stephan
Addition to: the quasi-Kronecker form for matrix pencils. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2012. - Online-Ressource (PDF-Datei: 7 S., 140,1 KB). . - (Preprint. - M12,8)
Eichfelder, Gabriele; Jahn, Johannes
Vector optimization problems and their solution concepts. - In: Recent developments in vector optimization. - Berlin [u.a.] : Springer, ISBN 978-3-642-21113-3, (2012), S. 1-27

Eichfelder, Gabriele;
Variable ordering structures in vector optimization. - In: Recent developments in vector optimization. - Berlin [u.a.] : Springer, ISBN 978-3-642-21113-3, (2012), S. 95-126

Behrndt, Jussi; Philipp, Friedrich; Trunk, Carsten
Bounds on the non-real spectrum of differential operators with indefinite weights. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2012. - Online-Ressource (PDF-Datei: 27 S., 276,8 KB). . - (Preprint. - M12,07)

Ordinary and partial differential operators with an indefinite weight function can be viewed as bounded perturbations of non-negative operators in Krein spaces. Under the assumption that 0 and infinity are not singular critical points of the unperturbed operator it is shown that a bounded additive perturbation leads to an operator whose non-real spectrum is contained in a compact set and with definite type real spectrum outside this set. The main results are quantitative estimates for this set, which are applied to Sturm-Liouville and second order elliptic partial differential operators with indefinite weights on unbounded domains.
Ilchmann, Achim;
Decentralized tracking of interconnected systems. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2012. - Online-Ressource (PDF-Datei: 18 S., 231,3 KB). . - (Preprint. - M12,06)

Decentralized funnel controllers are applied to finitely many interacting single-input single-output, minimum phase, relative degree one systems in order to track reference signals of each system within a prespecified performance funnel. The reference signals as well as the systems belong to a fairly large class. The result is a generalization of the work by [2].
Eichfelder, Gabriele;
Numerical procedures in multiobjective optimization with variable ordering structures. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2012. - Online-Ressource (PDF-Datei: 24 S., 365 KB). . - (Preprint. - M12,05)

Multiobjective optimization problems with a variable ordering structure instead of a partial ordering have recently gained interest due to several applications. In the last years a basic theory has been developed for such problems. The difficulty in their study arises from the fact that the binary relations of the variable ordering structure, which are defined by a cone-valued map which associates to each element of the image space a pointed convex cone of dominated or preferred directions, are in general not transitive. - In this paper we propose numerical approaches for solving such optimization problems. For continuous problems a method is presented using scalarization functionals which allows the determination of an approximation of the infinite optimal solution set. For discrete problems the Jahn-Graef-Younes method known from multiobjective optimization with a partial ordering is adapted to allow the determination of all optimal elements with a reduced effort compared to a pairwise comparison.
Berger, Thomas; Halikias, George; Karcanias, Nicos
Effects of dynamic and non-dynamic element changes in RLC networks. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2012. - Online-Ressource (PDF-Datei: 27 S., 328 KB). . - (Preprint. - M12,04)

The paper deals with the redesign of passive electric networks by changes of single dynamic and non-dynamic elements which may retain, or affect the natural topology of the network. It also deals with the effect of such changes on the natural dynamics of the network, the natural frequencies. The impedance and admittance modeling for passive electrical networks is used which provides a structured, symmetric, integral-differential description, which in the special cases of RC and RL networks is reduced to matrix pencil descriptions. The transformations on the network are expressed as those preserving, or modifying the two natural topologies of the network, the impedance graph and the admittance graph topologies. For the special cases of RC and RL networks we consider the problem of the effect of changes of a single dynamic, or non-dynamic element on the natural frequencies. Using the Determinantal Assignment Framework, it is shown that the family of single parameter variation problems is reduced to equivalent Root Locus problems with the possibility of fixed modes. An explicit characterization of the fixed modes is given and a number of interesting properties of the spectrum are derived such as the interlacing property of poles and zeros for the entire family of Root Locus problems.
Berger, Thomas; Ilchmann, Achim; Trenn, Stephan
The quasi-Weierstraß form for regular matrix pencils. - In: Linear algebra and its applications : LAA.. - New York, NY : American Elsevier Publ., Bd. 436 (2012), 10, S. 4052-4069
Harant, Jochen; Kemnitz, Arnfried; Saito, Akira; Schiermeyer, Ingo
Closures, cycles, and paths. - In: Journal of graph theory. - New York, NY [u.a.] : Wiley, ISSN 1097-0118, Bd. 69 (2012), 3, S. 314-323
Ilchmann, Achim; Pham Huu Anh, Ngoc
Stability and robust stability of positive Volterra systems. - In: International journal of robust and nonlinear control : IFAC affiliated journal.. - New York, NY [u.a.] : Wiley, ISSN 1099-1239, Bd. 22 (2012), 6, S. 604-629