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Tobias Damm: Publications


The files to be downloaded from this site are preprints and may differ from the printed articles. 


T. Damm, Rational Matrix Equations in Stochastic Control,  (Springer Lecture Notes in Control and Information Sciences, vol 297, 2004Zentralblatt Nr 1034.93001)


  1. V.I. Arnold: Vorlesungen über partielle Differentialgleichungen (Übersetzung aus dem Russischen)
    (seit März 2004 bei Springer, Zentralblatt Nr 1076.35001)
  2. V.I. Arnold: Gewöhnliche Differentialgleichungen (Übersetzung aus dem Russischen)
    (seit März 2001 bei Springer, Zentralblatt Nr 1049.34001)


Recently submitted manuscripts

  1. T. Damm, K. Sato, and A. Vierling: Numerical solution of Lyapunov equations related to Markov jump linear systems, March 2017, arXiv

Articles in Scientific Journals

  1. T. Damm, P. BennerJ. Hauth: Computing the Stochastic H-infinty-Norm by a Newton iteration, IEEE Control Systems Letters, 1(1), 92-97, (2017) arXiv
  2. H. Mena, T. Damm, T. Stillfjord: Numerical Solution of the Finite Horizon Stochastic Linear Quadratic Control Problem, Numer. Linear Algebra Appl., (2017) DOI:10.1002/nla.2091
  3. P. Benner, T. Damm, Y. Rodriguez Cruz  Dual pairs of generalized Lyapunov inequalities and balanced truncation of stochastic linear systems, IEEE TAC, 62, 782-791, (2017), arXiv
  4. P. Benner, T. Damm, M. Redmann, Y. Rodriguez Cruz: Positive operators and stable truncation, Preprint, Linear Algebra Appl. 498, 74-87, (2016)
  5. T. Damm, L. Grüne, M. Stieler, K. Worthmann: An exponential turnpike theorem for dissipative optimal control problems (.pdf), SIAM J. Control Optim. 52(3):1935-1957, 2014
  6. T. Damm and L. Muhirwa, Zero crossings, overshoot and initial undershoot in the step and impulse responses of linear systems (.pdf), IEEE Transactions of Automatic Control, 2014, 10.1109/TAC.2013.2294616
  7. E. Jarlebring, T. Damm and W. Michiels, Model reduction of time-delay systems using position balancing and delay Lyapunov equations (.pdf),  Math. Control Signals Syst. 25(2): 147-166, 2013
  8. T. Damm and D. Stahl, Linear least squares problems with additional constraints and an application to scattered data approximation, (.pdf), Linear Algebra Appl. 439(4), 933-943, 2013
  9. P. Benner, T. Breiten and T. Damm, Generalized Tangential Interpolation for Model Reduction of Discrete-Time MIMO Bilinear Systems (.pdf), Int. J. Control 84(8), 1398-1407, 2011.
  10. P. Benner and T. Damm, Lyapunov equations, energy functionals, and model order reduction of bilinear and stochastic systems (.pdf), SIAM J. Control Optim. 49(2):686-711, 2011
  11. T. Breiten and T. Damm, Krylov subspace methods for model order reduction of bilinear control systems (.pdf), Syst. Control Lett. 59(8):443-450, 2010
  12. T. Damm and H. Wimmer, A cancellation property of the Moore-Penrose inverse of triple products (.pdf), J. Austral. Math. Soc., 86(1):33-44, 2009
  13. T. Damm, Direct methods and ADI preconditioned Krylov subspace methods for generalized Lyapunov equations (.pdf), Numer. Linear Algebra Appl., 15(9):853-871, 2008
  14. E. Jarlebring, T. Damm, The Lambert W function and the spectrum of some multidimensional time-delay systems (.pdf), Automatica 43, 2124-2128, 2007
  15. T. Damm, On detectability of stochastic systems (.pdf), Automatica 43, 928-933, 2007
  16. H. Crauel, T. Damm, A.Ilchmann: Stabilization of linear systems by rotation (.pdf),
    Journal of Differential equations, 234:412-438, 2007
  17. V. Dragan, T. Damm, and G. Freiling: Lyapunov iterations for coupled Riccati differential equations arising in connection with Nash differential games (.pdf), Mathematical Reports, 9(59), 1: 35-46, 2007
  18. V. Dragan, T. Damm, G. Freiling, and T. Morozan: Differential equations with positive evolutions and some applications (.pdf), Results in Mathematics, 48: 206-235, 2005
  19. T. Damm: Groups of positive operators on the space of Hermitian matrices are completely positive (.pdf) Linear Algebra Appl.,393:127-137, 2004
  20. T. Damm, D. Hinrichsen: Newton's method for concave operators with resolvent positive derivatives in ordered Banach spaces, (.pdf) Linear Algebra Appl.,363:43-64, 2003
  21. T. Damm: Minimal representations of inverted Sylvester and Lyapunov operators (.pdf), Linear Algebra Appl.,363:35-41, 2003
  22. T. Damm: State-feedback $H^\infty$-type control of linear systems with time-varying parameter uncertainty (.pdf) Linear Algebra Appl.,351-352:185-210, 2002
  23. T. Damm, D. Hinrichsen: Newton's method for a rational matrix equation occuring in stochastic control (.pdf), Linear Algebra Appl.,332-334:81-109, 2001


Book Chapters and Proceedings

  1. T. Damm and P. Benner, Balanced Truncation for Stochastic Linear Systems with Guaranteed Error Bound (.pdf), MTNS 2014
  2. T. Damm and L. Muhirwa, On Euclidean Norm Balancing (.pdf), PAMM 13(1):487-488, 2013
  3. C. Grußler and T. Damm, A Symmetry Approach for Balanced Truncation of Positive Linear Systems (.pdf), CDC 2012
  4. T. Damm, Euclidean Norm Optimal Realization Revisited (.pdf), in Mathematical System Theory - Festschrift in Honor of Uwe Helmke on the Occasion of his 60th Birthday, K. Hüper and J. Trumpf (eds.), 2012
  5. D. Stahl and T. Damm, Approximation of scattered data using the lifting scheme (.pdf) PAMM 12(1):739-740, 2012
  6. T. Damm and L. Muhirwa, Zero crossings in the step response of linear time-delay systems (.pdf) PAMM 12(1):701-702, 2012
  7. C. Grußler and T. Damm, Symmetric Positivity Preserving Balanced Truncation (.pdf) PAMM 12(1):717-718, 2012
  8. T. Damm and J. Homeyer, On indefinite damping and gyroscopic stabilization (.pdf), in: Proc. 18th IFAC World Congr., (2011).
  9. P. Benner, T. Breiten and T. Damm, On H2-model reduction of linear parameter-varying systems (.pdf) PAMM 11(1):811-812, 2011
  10. T. Damm and J. Homeyer, Gyroscopic Stabilization of 2nd-Order-Systems with Indefinite Damping (.pdf) PAMM 11(1):805-806, 2011
  11. A State-Space Implementation of Anti-Causal Iterative Learning Control (with Urs Becker)
    (PAMM, Proceedings Appl. Math. Mech., 10:599-600, 2010)
  12. Krylov Subspace Methods for Model Order Reduction of Bilinear Discrete-Time Control Systems (with Peter Benner and Tobias Breiten)
    (PAMM, Proceedings Appl. Math. Mech., 10:601-602, 2010)
  13. Detectability, Observability, and Asymptotic Reconstructability of Positive Systems
    (with C. Ethington, in Springer Lecture Notes in Control and Information Sciences, vol 389, 2009)
  14. Reconstruction of shape using gradient measuring optical systems, (with J. Seewig, J. Frasch, D. Kauven, S. Rau, and J. Schnebele. Proceedings of FRINGE '09, 6th International Workshop on Advanced Optical Metrology, 2009)
  15. Stabilization of linear systems by dynamic high-gain rotation, .pdf
    (with H. Crauel and A.Ilchmann; Proceedings IFAC World Congress 2005, Praha)
  16. On double Newton steps, .pdf
    (Proceedings MTNS 2004, Leuven)
  17. Stability of linear systems and positive semigroups of symmetric matrices, .pdf
    (in "Positive Systems" Springer Lecture Notes in Control and Information Sciences, vol 294)
  18. A car-steering problem with random adhesion coefficient, .pdf
    (PAMM, Proceedings Appl. Math. Mech., 2:83-84, 2003)
  19. State-feedback $H^\infty$-control of stochastic linear systems
    (Proceedings of the 3rd NICONET Workshop 2001, Louvain-la-Neuve, Belgium)
  20. Generalized Riccati equations and stabilization of stochastic systems, .pdf
    (Proceedings CAO 2000, St. Petersburg)
  21. On the parameter dependence of a class of rational matrix equations occuring in stochastic optimal control, .pdf (with D. Hinrichsen; Proceedings MTNS 2000, Perpignan)
  22. On a rational matrix equation occuring in stochastic control, .pdf
    (with D. Hinrichsen; Proceedings ECC 1999, Karlsruhe)
  23. Matrix (in)equalities for linear stochastic systems, .pdf
    (with D. Hinrichsen; Proceedings MTNS 1998, Padua)


  1. Rational Matrix Equations in Stochastic Control, .pdf
    (Doktorarbeit (Bremen 2002), extended version appeared in LNCIS)
  2. Frequenzmethoden und Abschätzung der Hausdorffdimension zur Stabilitätsuntersuchung
    (Diplomarbeit (Würzburg 1996), see corresponding preprints below)

Preprints, Reports (not published or submitted elsewhere)

  1. Gewöhnliche Differentialgleichungen: Hausdorffdimension und Zhukowskijstabilität, .pdf
    (Preprint Nr. 221, Math. Inst., Univ. Würzburg, 1997)
  2. Der Frequenzsatz von Kalman-Jakubovich mit einer Anwendung zur Abschätzung singulärer Werte, .pdf
    (Preprint Nr. 220, Math. Inst., Univ. Würzburg, 1997)