home  about us  research  people  publications  vacancies  seminars  events  contact


Hamilton Logo

Publications of Fabian Wirth

This page is still under construction.

Please send comments to: fabian.wirth@nuim.ie

Home

On-line Publications

This page has been organised into five categories: The papers appear in reverse chronological order, so that the newer papers appear earlier.

Submissions

  1. F. Camilli, A. Cesaroni, L. Grüne, and F. Wirth.
    Stabilization of controlled diffusions via Zubov's method.
    submitted, August 2005.
  2. R. Shorten, F. Wirth, O. Mason, K. Wulff and C. King.
    Stability criteria for switched and hybrid systems.
    submitted, June 2005.
    pdf version
  3. S. Dashkovskiy, B.S. Rüffer, F.R. Wirth.
    An ISS Small-Gain Theorem for General Networks.
    submitted, June 2005.
    Technical Report 05-05, Zentrum für Technomathematik, Universität Bremen, 2005.
    gzipped postscript version pdf version  
  4. F. Wirth, R. Stanojevic, R. Shorten, and D. Leith.
    Stochastic equilibria of AIMD communication networks.
    submitted. December, 2004.
  5. F. Camilli, L. Grüne, and F. Wirth.
    Control Lyapunov functions and Zubov's method.
    submitted. May, 2004.

Books

  1. F. Colonius, U. Helmke, D. Prätzel-Wolters, F. Wirth, eds.,
    Advances in Mathematical Systems Theory, Birkhäuser, Boston, 2000.
    Birkhäuser's information page  

Journal Papers and Book Chapters

  1. R. Shorten, F. Wirth, and D. Leith.
    A positive systems model of TCP-like congestion control: Asymptotic results.
    IEEE/ACM Transactions on Networking. accepted for publication.
    pdf version
  2. N. Guglielmi, F. Wirth, and M. Zennaro.
    Complex polytope extremality results for families of matrices.
    SIAM Journal on Matrix Analysis and its Applications. 27:721-743, 2006.
    gzipped postscript version  pdf version
  3. F. Wirth.
    A converse Lyapunov theorem for linear parameter varying and linear switching systems.
    SIAM Journal on Control and Optimization. 44:210-239, 2005.
    Abstract   (gzipped postscript version, 279 KB)   (pdf version, 360 KB)
  4. F. Wirth.
    The generalized spectral radius is strictly increasing.
    Linear Algebra and its Applications, 395:141-153, 2005.
    Abstract   (gzipped postscript version, 155 KB)   (pdf version, 153 KB)
  5. F. Wirth.
    On Lipschitz continuity of the top Lyapunov exponent of linear parameter varying and linear switching systems.
    Stochastics and Dynamics, 4(3):461-481, 2004.
    Abstract   (gzipped postscript version, 195 KB)   (pdf version, 213 KB)
  6. D. Hinrichsen, E. Plischke, and F. Wirth.
    Robustness of Transient Behavior.
    In: V. D. Blondel, A. Megretski, eds., Unsolved Problems in Mathematical Systems and Control Theory. Princeton University Press, Princeton, NJ, 2004. pp. 197-202.
    (The relevant chapter in pdf)  
  7. C. Pötzsche, S. Siegmund, and F. Wirth.
    A Spectral Characterization of Exponential Stability for Linear Time-Invariant Systems on Time Scales.
    Discrete and Continuous Dynamical Systems - Series A, 9(5):1223-1241, 2003.
    (gzipped postscript version, 213 KB)  
  8. F. Wirth.
    The generalized spectral radius and extremal norms.
    Linear Algebra and its Applications, 342:17-40, 2002.
    Abstract   (gzipped postscript version, 101 KB)   (pdf version, 279 KB)
  9. F. Wirth.
    A linearization principle for robustness with respect to time-varying perturbations.
    in Dynamics, Bifurcations and Control, F. Colonius and L. Grüne, eds., Springer, Berlin, 2002. pp. 191- 200.
    (gzipped postscript version, 63 KB)  
  10. F. Camilli, L. Grüne, and F. Wirth.
    A generalization of Zubov's method to perturbed systems.
    SIAM Journal of Control and Optimization, 40(2):496-515, 2002.
    Abstract   (gzipped postscript version, 117 KB)   (pdf version, 265 KB)
  11. F. Wirth.
    Asymptotic behavior of the value functions of discrete-time discounted optimal control.
    Journal of Optimization Theory and its Applications, 110(1):183-210, 2001.
    Abstract   (gzipped postscript version, 76 KB)   (pdf version, 258 KB)
  12. U. Helmke and F. Wirth.
    On controllability of the real shifted inverse power iteration.
    Systems and Control Letters, 43(1):9-23, 2001.
    Abstract   (gzipped postscript version, 75 KB)   (pdf version, 263 KB)
  13. A.D.B. Paice and F.R. Wirth.
    Robustness of nonlinear systems and their domains of attraction.
    Chapter 3 in Advances in Mathematical Systems Theory, F. Colonius et al., eds., Birkhäuser, Boston, 2000. pp. 31 - 54.
    Abstract   (gzipped postscript version, 113 KB)   (pdf version, 238 KB)
  14. J. Behrens and F. Wirth.
    A globalization procedure for locally stabilizing controllers.
    in Nonlinear Control in the Year 2000, A. Isidori et al., eds., Lecture Notes in Control and Information Sciences, Vol. 258, Springer-Verlag, London, 2000, pp. 171 - 182.
    Abstract   (gzipped postscript version, 180 KB)   (pdf version, 360 KB)
  15. U. Helmke and F. Wirth.
    Controllability Properties of Numerical Eigenvalue Algorithms.
    in Nonlinear Control in the Year 2000, A. Isidori et al., eds., Lecture Notes in Control and Information Sciences, Vol. 258, Springer-Verlag, London, 2000, 467 - 480.
    (gzipped postscript version, 80 KB)   (pdf version, 198 KB)
  16. F. Camilli, L. Grüne, and F. Wirth.
    A regularization of Zubov's equation for robust domains of attraction.
    in Nonlinear Control in the Year 2000, A. Isidori et al., eds., Lecture Notes in Control and Information Sciences, Vol. 258, Springer-Verlag, London, 2000, pp. 277 - 290.
    Abstract   (gzipped postscript version, 117 KB)   (pdf version, 267 KB)
  17. L. Grüne and F. Wirth.
    On the rate of convergence of infinite horizon discounted optimal value functions.
    Nonlinear Analysis, Real World Applications, 1:499-515, 2000.
    Abstract   (gzipped postscript version, 161 KB)   (pdf version, 317 KB)
  18. L. Grüne, E.D. Sontag, and F.R. Wirth.
    Asymptotic stability equals exponential stability, and ISS equals finite energy gain---if you twist your eyes.
    Systems and Control Letters, 38(2):127-134, 1999.
    Abstract   (gzipped postscript version, 105 KB)   (pdf version, 237 KB)
  19. L. Grüne and F. Wirth.
    Feedback stabilization of discrete-time homogeneous semi-linear systems.
    Systems and Control Letters, 37(1):19-30, 1999.
    Abstract   (gzipped postscript version, 114 KB)   (pdf version, 248 KB)
  20. F. Colonius, D. Hinrichsen, and F. Wirth.
    Lyapunov exponents and robust stabilization.
    In V.D. Blondel, E.D. Sontag, M. Vidyasagar, and J.C. Willems, editors,
    Open Problems in Mathematical Systems and Control Theory ,
    Communications and Control Engineering Series, chapter~18, pages 83-88. Springer-Verlag, London, 1998.
    (gzipped postscript version, 61 KB)   (pdf version, 136 KB)
  21. A.D.B. Paice and F.R. Wirth.
    Analysis of the Local Robustness of Stability for Flows.
    Mathematics of Control, Signals and Systems, 11(4):289-302, 1998.
    Abstract   (gzipped postscript version, 114 KB)   (pdf version, 245 KB)
  22. F. Wirth.
    On stability of infinite-dimensional discrete inclusions.
    Summary in Journal of Mathematical Systems, Estimation, and Control. 8(4):507-510, 1998.
    Abstract Full electronic manuscript, 21 pp. (pdf version, 245 KB)
  23. F. Wirth.
    On the calculation of real time-varying stability radii.
    International Journal of Robust and Nonlinear Control. 8:1043-1058, 1998.
    Abstract   (gzipped postscript version, 119 KB)   (pdf version, 251 KB)
  24. E.D. Sontag and F.R. Wirth.
    Remarks on universal nonsingular controls for discrete-time systems.
    Systems and Control Letters, 33(2):81-88,1998.
    Abstract   (gzipped postscript version, 98 KB)   (pdf version, 221 KB)
  25. F. Wirth.
    Dynamics of time-varying discrete-time linear systems: Spectral theory and the projected system.
    Siam Journal of Control and Optimization, 36(2):447-487, 1998.
    Abstract   (gzipped postscript version, 210 KB)   (pdf version, 463 KB)
    Zentralblatt Review 
  26. F. Wirth.
    Remarks on 'Equivalence of stability concepts for discrete time-varying systems'.
    International Journal of Robust and Nonlinear Control, 8:91-93, 1998.
    Zentralblatt Review 
  27. F. Wirth and D. Hinrichsen.
    On stability radii of infinite dimensional time-varying discrete-time systems.
    IMA Journal of Mathematical Control and Information, 11:253-276, 1994.
    Abstract   (gzipped postscript version, 137 KB)   (pdf version, 282 KB)
    Zentralblatt Review 
  28. F. Wirth.
    Convergence of the value functions of discounted infinite horizon optimal control problems with low discount rates.
    Mathematics of Operations Research, 18(4):1006-1019, 1993.
    Zentralblatt Review 

Conference Papers

  1. E. Plischke, F. Wirth, and N. Barabanov.
    Duality results for the joint spectral radius and transient behavior.
    Proc. Joint Conference on Decision and Control and European Control Conference CDC/ECC 2005, Seville, Spain, December 2005, pp. 2344-2349.
    (pdf version)
  2. S. Dashkovskiy, B. S. Rüffer, and F. R. Wirth.
    A small-gain type stability criterion for large scale networks of ISS systems.
    Proc. Joint Conference on Decision and Control and European Control Conference CDC/ECC 2005, Seville, Spain, December 2005, pp. 5633-5638.
    (pdf version)
  3. F. Wirth.
    On the structure of the set of extremal norms of a linear inclusion.
    Proc. Joint Conference on Decision and Control and European Control Conference CDC/ECC 2005, Seville, Spain, December 2005, pp. 3019-3024.
    (pdf version)
  4. F. Wirth.
    A converse Lyapunov theorem for switched linear systems with dwell times.
    Proc. Joint Conference on Decision and Control and European Control Conference CDC/ECC 2005, Seville, Spain, December 2005, pp. 4572-4577.
    (pdf version)
  5. K. Wulff, F. Wirth, and R. Shorten.
    On the stabilisation of a class of SISO switched linear systems.
    Joint Conference on Decision and Control and European Control Conference CDC/ECC 2005, Seville, Spain, December 2005, pp. 3976-3981.
  6. F. Camilli, L. Grüne, and F. Wirth.
    Zubov's method for stochastic control systems.
    Proc. 16th IFAC World Congress, Prague, Czech Republic, July 2005, paper Mo-M20-TO/4 (CD-Rom).
  7. F. Wirth.
    The Gelfand formula for linear parameter varying and linear switching systems.
    Proc. 16th IFAC World Congress, Prague, Czech Republic, July 2005, paper Th-M12-TO/6 (CD-Rom).
  8. F. Camilli, L. Grüne, and F. Wirth.
    Calculating the domain of attraction: Zubov's method and extensions.
    Proc. SCP 2005, Stability and Control Processes, dedicated to the 75th birthday of V.I. Zubov, St. Petersburg, Russia, June 2005, pp. 27-36.
  9. S. Dachkovski, F. Wirth, and T. Jagalski.
    Autonomous control of shop floor logistics: Analytic models.
    in: J. Chryssolouris, D. Mourtzis (eds.), Manufacturing, Modelling, Management and Control 2004, IFAC Workshop Series, Elsevier Science, Amsterdam, 2005.
  10. F. Camilli, L. Grüne, and F. Wirth.
    Construction of Lyapunov functions on the domain of asymptotic nullcontrollability: theory.
    6th IFAC Nonlinear Control Systems Design Symposium NOLCOS 2004, Stuttgart, Germany, pp. 877-882, September 2004.
  11. F. Camilli, L. Grüne, and F. Wirth.
    Construction of Lyapunov functions on the domain of asymptotic nullcontrollability: numerics.
    6th IFAC Nonlinear Control Systems Design Symposium NOLCOS 2004, Stuttgart, Germany, pp. 883-888, September 2004.
  12. E. Plischke, F. Wirth.
    Stabilization of linear systems with prescribed transient bounds.
    Symposium on Mathematical Theory of Networks and Systems MTNS-2004, Katholieke Universiteit Leuven, Belgium, July 2004, paper no. 181 (CD-Rom).
      (pdf version)
  13. F. Wirth.
    Transient behavior and robustness.
    Symposium on Mathematical Theory of Networks and Systems MTNS-2004, Katholieke Universiteit Leuven, Belgium, July 2004, paper no. 339 (CD-Rom).
    Abstract     (pdf version)
  14. F. Camilli, L. Grüne, and F. Wirth.
    Characterizing controllability probabilities of stochastic control systems via Zubov's method.
    Symposium on Mathematical Theory of Networks and Systems MTNS-2004, Katholieke Universiteit Leuven, Belgium, July 2004, paper no. 65 (CD-Rom).
        (pdf version)
  15. F. Wirth.
    A monotonicity property of the joint spectral radius.
    Symposium on Mathematical Theory of Networks and Systems MTNS-2004, Katholieke Universiteit Leuven, Belgium, July 2004, paper no. 60 (CD-Rom).
    Abstract     (pdf version)
  16. F. Wirth.
    Applications of Zubov's method to perturbed systems.
    In B. Lohmann, A. Gräser, eds.: Methods and Applications in Automation, 24th Colloquium of Automation, Salzhausen, Germany, Shaker Verlag, Aachen, 2003, pages 14-23.
  17. F. Wirth.
    Stability of linear parameter varying and linear switching systems.
    PAMM, Proceedings in Applied Mathematics and Mechanics, 3(1):144-147, 2003.
    (gzipped postscript version, 109 KB)   (pdf version, 127 KB)
  18. F. Camilli, L. Grüne, and F. Wirth.
    A generalization of Zubov's method to perturbed systems.
    Proc. 41st IEEE Conference on Decision and Control, CDC2002, Las Vegas, NV, US, pp. 3518-3523, 2002.
    Abstract   (gzipped postscript version, 70 KB)   (pdf version, 191 KB)
  19. F. Wirth.
    A genericity result for time-varying stability radii using nonsmooth analysis.
    Proc. 41st IEEE Conference on Decision and Control, CDC2002, Las Vegas, NV, US, 2002.
  20. D. Hinrichsen, E. Plischke, and F. Wirth.
    State Feedback Stabilization with Guaranteed Transient Bounds.
    Proc. Symposium on Mathematical Theory of Networks and Systems MTNS-2002, South Bend, IN, US, 2002, (CD-ROM), paper 2132.
    Abstract   (gzipped postscript version, 69 KB)   (pdf version, 173 KB)
  21. F. Wirth.
    Parameter Dependent Extremal Norms for Linear Parameter Varying Systems.
    Proc. Symposium on Mathematical Theory of Networks and Systems MTNS-2002, South Bend, IN, US, 2002, (CD-ROM), paper 9024.
    Abstract   (gzipped postscript version, 83 KB)   (pdf version, 193 KB)
  22. F. Wirth.
    On Lipschitz continuity of the joint spectral radius.
    PAMM, Proceedings in Applied Mathematics and Mechanics, 1:109-110, 2002.
    Abstract   (gzipped postscript version, 31 KB)   (pdf version, 94 KB)
  23. L. Grüne and F. Wirth.
    Computing control Lyapunov functions via a Zubov type algorithm.
    Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia    , 2129 - 2134, 2000.
    Abstract   (gzipped postscript version, 47 KB)   (pdf version, 183 KB)
  24. F. Camilli, L. Grüne, and F. Wirth.
    Zubov's method for perturbed differential equations.
    Proceedings of the Symposium on Mathematical Theory of Networks and Systems MTNS-2000, Perpignan, France, 2000. (CD-ROM) paper B100.
    Abstract   (gzipped postscript version, 49 KB)   (pdf version, 122 KB)
  25. F. Wirth.
    Exponential stability of families of linear delay systems.
    Proceedings of the Symposium on Mathematical Theory of Networks and Systems MTNS-2000, Perpignan, France, 2000. (CD-ROM) paper B06.
    Abstract   (gzipped postscript version, 31 KB)   (pdf version, 86 KB)
  26. F. Wirth.
    Further results on the Lyapunov spectrum of time-varying linear discrete-time systems.
    Proceedings of the Symposium on Mathematical Theory of Networks and Systems MTNS-2000, Perpignan, France, 2000. (CD-ROM) paper B05.
    Abstract   (gzipped postscript version, 34 KB)   (pdf version, 94 KB)
  27. L. Grüne, E.D. Sontag, and F. Wirth.
    On the equivalence between asymptotic and exponential stability, and between ISS and finite $H_\infty$ gain.
    Proceedings of the 38th IEEE Conference on Decision and Control, USA, 1200 - 1205, 1999.
    Abstract   (gzipped postscript version, 46 KB)   (pdf version, 189 KB)
  28. N. Siebel, 0. Lang, F. Wirth, A. Gräser.
    Robuste Positionierung eines Roboters mittels Visual Servoing unter Verwendung einer Trust-Region-Methode.
    In: Deutsche Forschungsvereinigung für Meß-, Regelungs- Systemtechnik e.V. (DFMRS), Jahrestagung 1999, Automatische Prozeßführung, Prozeßüberwachung und Montage, Bremen, Germany, 11.-12. November 1999, pp.23-39.
    (gzipped postscript version, 886 KB)   (pdf version, 798 KB)
  29. U. Helmke and F. Wirth.
    Controllability of the shifted inverse power iteration: The case of real shifts.
    In B. Fiedler et al. eds., International Conference on Differential Equations, Equadiff 99, Berlin, 1999. Vol. 2. pp. 859 - 864. World Scientific, Singapore, 2000.
    Abstract   (gzipped postscript version, 75 KB)   (pdf version, 179 KB)
  30. L. Grüne, E.D. Sontag, and F.R. Wirth.
    On equivalence of exponential and asymptotic stability under changes of variables.
    In B. Fiedler et al. eds., International Conference on Differential Equations, Equadiff 99, Berlin, 1999. Vol. 2. pp. 850 - 852. World Scientific, Singapore, 2000.
    (gzipped postscript version, 63 KB)   (pdf version, 152 KB)
  31. M. Falcone, L. Grüne, and F. Wirth.
    A maximum time approach to the computation of robust domains of attraction.
    In B. Fiedler et al. eds., International Conference on Differential Equations, Equadiff 99, Berlin, 1999. Vol. 2. pp. 844 - 849. World Scientific, Singapore, 2000.
    Abstract   (gzipped postscript version, 96 KB)   (pdf version, 170 KB)
  32. F. Wirth.
    Stabilität und Stabilisierung periodischer Systeme.
    20. Kolloquium der Automatisierungstechnik, Salzhausen 1998. In B. Lohmann, A. Gräser (Hrsg.): Methoden und Anwendungen der Automatisierungstechnik, S. 43 - 51, Shaker Verlag, Aachen, 1999.
    (gzipped postscript version, 57 KB)  
  33. L. Grüne and F. Wirth.
    On Linear Convergence of Discounted Optimal Control Problems with Vanishing Discount Rate.
    Proceedings of the Symposium on Mathematical Theory of Networks and Systems MTNS-98, Padova, Italy, 185 - 188, 1998.
    (gzipped postscript version, 73 KB)   (pdf version, 181 KB)
  34. A.D.B. Paice and F. Wirth.
    Robustness analysis of domains of attraction of nonlinear systems.
    Proceedings of the Symposium on Mathematical Theory of Networks and Systems MTNS-98, Padova, Italy, 353 - 356, 1998.
    (gzipped postscript version, 77 KB)   (pdf version, 185 KB)
  35. F. Wirth.
    Dynamics and controllability of nonlinear discrete-time control systems.
    Preprints of the 4th IFAC Nonlinear Control Systems Design Symposium, NOLCOS98, Enschede, The Netherlands, 269 - 275, 1998.
    Abstract   (gzipped postscript version, 57 KB)   (pdf version, 127 KB)
  36. A.D.B. Paice and F.R. Wirth.
    Robustness of nonlinear systems subject to time-varying perturbations.
    Proceedings of the 36th Conference on Decision and Control, San Diego, California, USA, 4436 - 4441, 1997.
    (gzipped postscript version, 69 KB)   (pdf version, 160 KB)
  37. F. Wirth.
    Computing time-varying stability radii via discounted optimal control.
    Proceedings of the 36th Conference on Decision and Control, San Diego, California, USA, 3278 - 3283, 1997.
    (gzipped postscript version, 83 KB)   (pdf version, 194 KB)
  38. A.D.B. Paice and F.R. Wirth.
    Analysis of the local robustness of stability for maps.
    Proceedings of the ECC'97, paper no. 334, session TU-E-B-4, Brussels, 1997.
    Abstract   (gzipped postscript version, 90 KB)   (pdf version, 205 KB)
  39. F. Wirth.
    Stability indices of infinite-dimensional discrete inclusions.
    Proceedings of the ECC'97, paper no. 394, session FR-M-E-5, Brussels, 1997.
    (gzipped postscript version, 86 KB)   (pdf version, 198 KB)
  40. D. Hinrichsen and F. Wirth.
    Lyapunov exponents of bilinear systems.
    Proceedings of the Workshop on Open Problems in Mathematical Systems Theory and Control, Liège, 42-45, 1997.
  41. A.D.B. Paice and F.R. Wirth.
    On robustness of nonlinear systems.
    Jahrestagung der Gesellschaft für angewandte Mathematik und Mechanik GAMM'97, Regensburg March 1997. ZAMM, Supplement 3:1029-1030, 1998.
  42. L. Grüne und F. Wirth.
    Feedback stabilization of semi-linear discrete-time systems.
    Jahrestagung der Gesellschaft für angewandte Mathematik und Mechanik GAMM'97, Regensburg March 1997. ZAMM, Supplement 3:925-926, 1998.
  43. F. Wirth.
    Universal controls for homogeneous discrete-time systems.
    In Proceedings of the 34th IEEE Conference on Decision and Control, New Orleans, Louisiana, USA, 25-26, 1995.
  44. F. Wirth.
    Lyapunov exponents of uncertain discrete-time systems.
    In Interval '94 St. Petersburg, Russia 1994, also appeared as The Floquet and Lyapunov spectra of discrete-time linear systems. Report 311, Institut für Dynamische Systeme, Universität Bremen 1994.

Other Publications

  1. F. Wirth.
    Stability Theory for Perturbed Systems.
    Habilitation Thesis, University of Bremen, January 2002.
  2. F. R. Wirth.
    Robust Stability of Discrete-Time Systems under Time-Varying Perturbations
    Dissertation, University of Bremen, July 1995.
    Zentralblatt Review 
  3. F. Wirth.
    An introduction to spectral theory of discrete-time linear time-varying systems. MTNS96, St. Louis, Missouri, 1996. Submitted to the Journal of Mathematical, Systems, Estimation, and Control. The refereeing process was not completed, when the Journal was discontinued.
    (gzipped postscript version, 126 KB)  

Home

Mathematics