Fachbereich Mathematik 
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Research areas

Infinite-dimensional systems, partial differential equations and partial differential-algebraic equations

  • adaptive control
  • linear-quadratic optimal control
  • numerical analysis of operator Lyapunov and Riccati equations
  • finite-dimensional approximation
  • infinite-dimensional differential-algebraic systems
Thomas Berger, Tobias Breiten, Marc Puche, Timo Reis
Funnel control for the monodomain equations with the FitzHugh-Nagumo model
Hamburger Beiträge zur Angewandten Mathematik 2019-12, Hamburg (2019) PDF, submitted
Marc Puche, Felix L. Schwenninger, Timo Reis
Funnel control for boundary control systems
aczepted for publication in Evol. Eq. Control Th. (2020) PDF
Marc Puche
Adaptive control for boundary control systems
Dissertation (2019) PDF
Arash Massoudi
Numerical algorithms for linear-quadratic optimal control of well-posed linear systems
Dissertation (2016) PDF
Timo Reis, Tilman Selig
Zero dynamics and root locus for a boundary controlled heat equation
Math. Control Signals Systems, 27(3), pp. 347-373 (2015) doi:10.1007/s00498-015-0143-4
Timo Reis, Tilman Selig
Funnel control for the boundary controlled heat equation
SIAM J. Control Optim., 53(1), pp. 547-574 (2015) doi:10.1137/140971567
Timo Reis, Tilman Selig
Balancing transformations for infinite-dimensional systems with nuclear Hankel operator
Integr. Equ. Oper. Theory 79(1), pp. 67-105 (2013) doi:10.1137/10.1007/s00020-013-2105-x
Mark R. Opmeer, Timo Reis, Winnifried Wollner
Finite-rank ADI iteration for operator Lyapunov equations
SIAM J. Control Optim., 51(5), pp. 4084-4117 (2013) doi:10.1137/120885310
Michael Hanke, Timo Reis
The perturbation and ADAE index of a degenerated hyperbolic system modelling a heat exchanger
Res. Math., 53(1-2), pp. 103-127 (2009) doi:10.1007/s00025-008-0304-6
Timo Reis
Controllability and observability of infinite dimensional descriptor systems
IEEE Trans. Automat. Control, 53(4), pp. 929-940 (2008) doi:10.1109/TAC.2008.920236
Timo Reis
Consistent initialization and perturbation analysis for abstract differential-algebraic equations
Math. Control Signals Systems, 19(3), pp. 255-281 (2007) doi:10.1007/s00498-007-0013-9
Timo Reis, Caren Tischendorf
Frequency domain methods and decoupling of linear infinite dimensional differential algebraic systems
J. Evol. Equ., 5(3), pp. 357-385 (2005) doi:10.1007/s00028-005-0198-7
Timo Reis
Systems theoretic aspects of PDAEs and applications to electrical circuits
Dissertation (2006), PDF

Control of differential-algebraic systems

  • adaptive control
  • linear-quadratic optimal control
  • observer design
  • applications in multibody dynamics
Timo Reis, Matthias Voigt
Linear-quadratic optimal control of differential-algebraic systems: The infinite time horizon problem with zero terminal state
SIAM J. Control Optim. 7(3), pp. 1567-1596 (2019) doi:10.1137/18M1189609
Lê Huy Hoàng
Funnel control for systems with known vector relative degree
Dissertation (2019) PDF
Thomas Berger, Svenja Otto, Timo Reis, Robert Seifried
Combined open-loop and funnel control for underactuated multibody systems
Nonlinear Dynamics 95(3), pp. 1977-1998 (2019) doi:10.1007/s11071-018-4672-5
Thomas Berger, Timo Reis
The funnel pre-compensator
Internat. J. Robust Nonlinear Control 28(16), pp. 4747-4771 (2018) doi:10.1002/rnc.4281
Marc Puche, Felix L. Schwenninger, Timo Reis
Constant-coefficient differential-algebraic operators and the Kronecker form
Linear Algebra Appl., 552, pp. 29-41 (2018) doi:10.1016/j.laa.2018.04.005
Thomas Berger, Timo Reis
Observers and dynamic controllers for linear differential-algebraic systems
SIAM J. Control Optim., 55(6), pp. 3564-3591 (2017) doi:10.1137/15M1035355
Thomas Berger, Timo Reis
Regularization of linear time-invariant differential-algebraic systems
Systems Control Lett., 78, pp. 40-46 (2015) doi:10.1016/j.sysconle.2015.01.013
Thomas Berger, Achim Ilchmann, Timo Reis
Zero dynamics and funnel control of linear differential-algebraic systems
Math. Control Signals Systems, 24(3), pp. 219-263 (2012) doi:10.1007/s00498-012-0085-z
Philip Losse, Volker Mehrmann, Lisa Poppe, Timo Reis
The modified optimal H control problem for descriptor systems
SIAM J. Control Optim., 48(4), pp. 2600-2619 (2009) doi:10.1137/070710093

Model reduction of dynamical systems

  • balanced truncation
  • passivity and structure preserving methods
  • applications to coupled systems and electrical circuits
Ines Dorschky, Timo Reis, Matthias Voigt
Balanced truncation model reduction for symmetric second order systems -- A passivity-based approach
Hamburger Beiträge zur Angewandten Mathematik 2020-14, Hamburg, submitted (2020) PDF
Mark R. Opmeer, Timo Reis
A lower bound for the balanced truncation error for MIMO systems
IEEE Trans. Automat. Control, 60(8), pp. 2207-2212 (2015) doi:10.1109/TAC.2014.2368232
Jens Möckel, Timo Reis, Tatjana Stykel
Linear-quadratic Gaussian balancing for model reduction of differential-algebraic systems
Internat. J. Control, 84(10), pp. 1627-1643 (2011) doi:10.1080/00207179.2011.622791
Athanasios C. Antoulas, Matthias Heinkenschloss, Timo Reis
Balanced truncation model reduction for systems with inhomogeneous initial conditions
Automatica, 47(3), pp. 559-564 (2011) doi:10.1016/j.automatica.2010.12.002
Timo Reis, Tatjana Stykel
Lyapunov balancing for passivity-preserving model reduction of RC circuits
SIAM J. Appl. Dyn. Syst., 10(1), pp. 1-34 (2011) doi:10.1137/090779802
Timo Reis, Jan C. Willems
A balancing approach to the realization of systems with internal passivity and reciprocity
Systems Control Lett., 60(1), pp. 69-74 (2011) doi:10.1016/j.sysconle.2010.10.009
Timo Reis, Tatjana Stykel
PABTEC: Passivity-preserving balanced truncation for electrical circuits
IEEE Trans. Computer-Aided Design Integr. Circuits Syst., 29(9), pp. 1354-1367 (2010) doi:10.1109/TCAD.2010.2059330
Timo Reis, Tatjana Stykel
Positive real and bounded real balancing for model reduction of descriptor systems
Internat. J. Control, 82(1), pp. 74-88 (2010) doi:10.1080/00207170903100214
Timo Reis, Elena Virnik
Positivity preserving balanced truncation for descriptor systems
SIAM J. Control Optim., 48(4), pp. 2600-2619 (2009) doi:10.1137/080734200
Timo Reis, Tatjana Stykel
Balanced truncation model reduction of second-order systems
Math. Comput. Model. Dyn. Syst., 14(5), pp. 391-406 (2009) doi:10.1080/13873950701844170
Timo Reis, Tatjana Stykel
Stability analysis and model order reduction for coupled systems
Math. Comput. Model. Dyn. Syst., 13(5), pp. 413-436 (2007) doi:10.1080/13873950701189071

Matrix equations in systems theory

  • Riccati and Lur'e equations
  • Kalman-Yakubovich-Popov inequality
  • low rank iterative methods
Arash Massoudi, Mark R. Opmeer, Timo Reis
The ADI method for bounded real and positive real Lur'e equations
Numerische Mathematik, 135(2), pp. 431-458 (2017) doi:10.1007/s00211-016-0805-2
Arash Massoudi, Mark R. Opmeer, Timo Reis
Analysis of an iteration method for the algebraic Riccati equation
SIAM. J. Matrix Anal. Appl., 37(2), pp. 624-648 (2016) doi:10.1137/140985792
Federico Poloni, Timo Reis
A structured doubling algorithm for Lur'e Equations
Numer. Linear Algebra Appl., 23(1), pp. 169-186 (2016) doi:10.1002/nla.2019
Timo Reis, Matthias Voigt
The Kalman-Yakubovich-Popov inequality for differential-algebraic systems: existence of nonpositive solutions
Systems Control Lett., 95 (Jan C. Willems Memorial Issue), pp. 3-10 (2016) doi:10.1016/j.sysconle.2016.05.010
Timo Reis, Olaf Rendel, Matthias Voigt
The Kalman-Yakubovich-Popov inequality for differential-algebraic systems
Linear Algebra Appl., 485, pp. 153-193 (2015) doi:10.1016/j.laa.2015.06.021
Federico Poloni, Timo Reis
A deflation approach for large-scale Lur'e equations
SIAM. J. Matrix Anal. Appl. 33(4), pp. 1339-1368 (2012) doi:10.1137/120861679
Timo Reis
Lur'e equations and even matrix pencils
Linear Algebra Appl., 434(1), pp. 152-173 (2011) doi:10.1016/j.laa.2010.09.005

Mathematical theory of electrical circuits

  • numerical simulation
  • structural analysis via graph theoretical approaches
  • circuit synthesis
Andreas Bartel, Michael Günther, Birgit Jacob, Timo Reis
Dynamic iteration schemes and port-Hamiltonian formulation in coupled DAE circuit simulation
Hamburger Beiträge zur Angewandten Mathematik 2020-12, Hamburg (2020) PDF, eingereicht
Hannes Gernandt, Frédéric E. Haller, Timo Reis, Arjan J. van der Schaft
Port-Hamiltonian formulation of nonlinear electrical circuits
Hamburger Beiträge zur Angewandten Mathematik 2020-09, Hamburg (2020) PDF, eingereicht
Fedor Glazov, Timo Reis
Systems theoretic properties of linear RLC circuits
Hamburger Beiträge zur Angewandten Mathematik 2020-01, Hamburg (2020) PDF, eingereicht
Timo Reis
Mathematical modeling and analysis of nonlinear time-invariant RLC circuits
P. Benner, R. Findeisen, D. Flockerzi, U. Reichl and K. Sundmacher (eds): Large-Scale Networks in Engineering and Life Sciences, S. 125-198
Modeling and Simulation in Science, Engineering and Technology, Birkhäuser, Basel, (2014) doi:10.1007/978-3-319-08437-4_2
Timo Reis
Circuit synthesis of passive descriptor systems - a modified nodal approach
Int. J. Circ. Theor. Appl., 38(1), S. 44-68 (2010) doi:10.1002/cta.532

  Seitenanfang  Impress 2020-06-29, Timo Reis