Mark Opmeer

Publications in Journals

• Chris Guiver, Hartmut Logemann and Mark R. Opmeer.
  A mixed passivity/small-gain theorem for Sobolev input-output stability.
  SIAM Journal on control and optimization, vol. 62 (2024), no. 6, pp 3042-3075. 
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• Chris Guiver and Mark R. Opmeer.
  The energy-balance method for optimal control in renewable energy applications.
  Renewable Energy Focus, vol. 50 (2024), article number 100582
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• Chris Guiver, Hartmut Logemann and Mark R. Opmeer.
  Operator-valued multiplier theorems for causal translation-invariant operators with applications to control theoretic input-output stability.
  Mathematics of Control, Signals, and Systems, vol. 36 (2024), pp 729–773.
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• Chris Guiver and Mark R. Opmeer.
  Representations and regularity of vector-valued right-shift invariant operators between half-line Bessel potential spaces.
  Integral Equations and Operator Theory, vol. 95 (2023), article number 19, 34 pages
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• Mark R. Opmeer.
  A convergence rate for the ADI method for infinite-dimensional Lyapunov equations.
  IFAC PapersOnLine, vol. 54 (2021), no. 9, pp 373-377.
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• Mark R. Opmeer.
  Decay of singular values for infinite-dimensional systems with Gevrey regularity.
  Systems and Control Letters, vol. 137 (2020).
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• Mark R. Opmeer and Olof J. Staffans.
  Optimal Control on the Doubly Infinite Time Axis for Well-Posed Linear Systems.
  SIAM Journal on control and optimization, vol. 57 (2019), no. 3, pp 1985-2015. 
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• Chris Guiver, Hartmut Logemann and Mark R. Opmeer.
  Infinite-dimensional Lur'e systems: input-to-state stability and convergence properties.
  SIAM Journal on control and optimization, vol. 57 (2019), no. 1, pp 334-365. 
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• Chris Guiver, Hartmut Logemann and Mark R. Opmeer.
  Transfer functions of infinite-dimensional systems: positive realness and stabilization.
  Mathematics of Control, Signals, and Systems, vol 29 (2017), no 2, 61 pages.
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• Arash Massoudi, Mark R. Opmeer and Timo Reis.
  The ADI method for bounded real and positive real Lur'e equations.
  Numerische Mathematik, vol 135 (2017), no 2, pp 431-458.
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• Arash Massoudi, Mark R. Opmeer and Timo Reis.
  Analysis of an iteration method for the algebraic Riccati equation.
  SIAM Journal on Matrix Analysis and Applications (SIMAX), vol 37 (2016), no 2, pp 624-648.
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  (a previous version of this article had the title The ADI method for algebraic Riccati equations)


• Amine N. Chakhchoukh and Mark R. Opmeer.
  The state space isomorphism theorem for discrete-time infinite-dimensional systems.
  Integral Equations and Operator Theory, vol 84 (2016), no. 1, pp 105-120. 
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• Mark R. Opmeer and Timo Reis.
  A lower bound for the balanced truncation error for MIMO systems.
  IEEE Transactions on Automatic Control, vol. 60 (2015), no. 8, pp 2207-2212.
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• Mark R. Opmeer and Olof J. Staffans.
  Optimal control on the doubly infinite continuous-time axis and coprime factorizations.
  SIAM Journal on control and optimization, vol. 52 (2014), no. 3, pp 1958-2007. 
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• Chris Guiver and Mark R. Opmeer.
  Model reduction by balanced truncation for systems with nuclear Hankel operators.
  SIAM Journal on control and optimization, vol. 52 (2014), no. 2, pp 1366-1401. 
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• Mark R. Opmeer, Timo Reis and Winnifried Wollner.
  Finite-rank ADI iteration for operator Lyapunov equations.
  SIAM Journal on control and optimization, vol. 51 (2013), no. 5, pp 4084-4117. 
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• Chris Guiver and Mark R. Opmeer.
  Error bounds in the gap metric for dissipative balanced approximations.
  Linear Algebra and its Applications, vol. 439 (2013), no. 12, pp 3659-3698. 
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• Chris Guiver and Mark R. Opmeer.
  Bounded real and positive real balanced truncation for infinite-dimensional systems.
  Mathematical Control and Related Fields, vol.3 (2013), no.1, pp 83-119. 
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• Mark R. Opmeer.
  Model order reduction by balanced proper orthogonal decomposition and by rational interpolation.
  IEEE Transactions on Automatic Control, vol.57 (2012), no.2, pp 472-477. 
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• Mark R. Opmeer and Olof J. Staffans.
  Coprime factorization and optimal control on the doubly infinite discrete time axis.
  SIAM Journal on control and optimization, vol. 50 (2012), no. 1, pp 266-285. 
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• Mark R. Opmeer.
  Infinite-dimensional negative imaginary systems.
  IEEE Transactions on Automatic Control, vol.56 (2011), no.12, pp 2973-2976. 
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• Ruth F. Curtain and Mark R. Opmeer.
  Coprime factorization and robust stabilization for discrete-time infinite-dimensional systems.
  Mathematics of Control, Signals, and Systems, vol.23 (2011) no.1-3, pp 101-115. 
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• Chris Guiver and Mark R. Opmeer.
  A counter-example to ''Positive realness preserving model reduction with H-infinity norm error bounds''.
  IEEE Transactions on Circuits and Systems I Regular Papers, vol.58 (2011), no.6, pp 1410-1411. 
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• Mark R. Opmeer and Olof J. Staffans.
  Optimal input-output stabilization of infinite-dimensional discrete time-invariant linear systems by output injection.
  SIAM Journal on control and optimization, vol. 48 (2010), no. 8, pp 5084-5107. 
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• Mark R. Opmeer.
  Decay of Hankel singular values of analytic control systems.
  Systems and control letters, vol.59 (2010), no.10, pp 635-638. 
  download preprint     journal version (see also the following correction)


• Chris Guiver and Mark R. Opmeer.
  Non-dissipative boundary feedback for Rayleigh and Timoshenko beams.
  Systems and control letters, vol.59 (2010), no.9, pp 578-586. 
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• Ruth F. Curtain and Mark R. Opmeer.
  State space formulas for a solution of the suboptimal Nehari problem on the unit disc.
  Integral equations and operator theory, vol.64 (2009), no.1, pp 35-59. 
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• Mark R. Opmeer and Olof J. Staffans.
  Optimal state feedback input-output stabilization of infinite-dimensional discrete time-invariant linear systems.
  Complex analysis and operator theory, vol. 2 (2008), no. 3, pp 479-510 . 
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• Mark R. Opmeer.
  Nuclearity of Hankel operators for ultradifferentiable control systems.
  Systems and control letters, vol. 57 (2008), no. 11, pp 913-918. 
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• Mark R. Opmeer.
  LQG balancing for continuous-time infinite-dimensional systems.
  SIAM Journal on control and optimization, vol.46 (2007), no. 5, pp 1831-1848.  
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• Mark R. Opmeer.
  Distribution semigroups and control systems.
  Journal of Evolution Equations, vol.6 (2006), no. 1, pp 145-159.  
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• Ruth F. Curtain and Mark R. Opmeer.
  Normalized doubly coprime factorizations for infinite-dimensional linear systems.
  Mathematics of Control, Signals, and Systems, vol.18 (2006) no.1, pp 1-31. 
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• Mark R. Opmeer.
  Infinite-dimensional linear systems: a distributional approach.
  Proceedings of the London Mathematical Society, vol. 91 (2005), no. 3, pp 738-760.  
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• Ruth F. Curtain and Mark R. Opmeer.
  The suboptimal Nehari problem for well-posed linear systems.
  SIAM Journal on control and optimization, vol. 44 (2005), no. 3, pp 991-1018. 
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• Mark R. Opmeer and Ruth F. Curtain.
  LQG-balancing for discrete-time infinite-dimensional linear systems.
  SIAM Journal on control and optimization, vol. 43 (2004), no. 4, pp 1196-1221. 
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• Mark R. Opmeer and Ruth F. Curtain.
  New Riccati equations for well-posed linear systems.
  Systems and control letters, vol. 52 (2004), no. 5, pp 339-347. 
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Publications in Conference Proceedings

• Mark R. Opmeer.
  Decay of singular values of the Gramians of infinite-dimensional systems.
  Proceedings of the ECC 2015, 6 pages.
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• Mark R. Opmeer.
  Optimal model reduction for non-rational functions.
  Proceedings of the ECC 2015, 6 pages.
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• Mark R. Opmeer.
  The algebraic Riccati equation for infinite-dimensional systems.
  Proceedings of the MTNS 2014, 5 pages.
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• Mark R. Opmeer.
  Model reduction for distributed parameter systems: a functional analytic view.
  Proceedings of the ACC 2012, 6 pages.
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• Chris Guiver and Mark R. Opmeer.
  Non-dissipative boundary feedback for elastic beams.
  Proceedings of the MTNS 2010, 4 pages.
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• Mark R. Opmeer and Orest V. Iftime.
  Representation of solutions of Riccati equations for well-posed systems.
  Proceedings of the MTNS 2010, 6 pages.
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• Ruth F. Curtain and Mark R. Opmeer.
  The Nehari problem for discrete-time infinite-dimensional systems.
  Proceedings of the ECC 2007, 6 pages.


• Mark R. Opmeer and Ruth F. Curtain.
  Non-well-posed infinite-dimensional linear systems.
  Proceedings of the CDC 2006, 6 pages.
  


• Mark R. Opmeer, Fred W. Wubs and Simon van Mourik.
  Model reduction for controller design for infinite-dimensional systems: theory and an example.
  Proceedings of the CDC 2005, 6 pages.
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• Mark R. Opmeer and Orest V. Iftime.
  A representation of all bounded selfadjoint solutions of the algebraic Riccati equation for systems with an unbounded observation operator.
  Proceedings of the CDC 2004, 6 pages.
  


• Ruth F. Curtain and Mark R. Opmeer.
  Normalized doubly coprime factorizations for state linear systems.
  Proceedings of the ASCC 2004, 9 pages.
  


• Mark R. Opmeer.
  The linear quadratic regulator problem for a large class of infinite-dimensional systems.
  Proceedings of the MTNS 2004, 8 pages.
  


• Ruth F. Curtain and Mark R. Opmeer.
  The suboptimal Nehari problem for stable infinite-dimensional linear systems: bridging the gap.
  Proceedings of the MTNS 2004, 19 pages.
  


• Mark R. Opmeer and Ruth F. Curtain.
  LQG-balancing in infinite dimensions.
  Proceedings of the MTNS 2002, 8 pages.
  

Theses

• Mark R. Opmeer
  Model reduction for controller design for infinite-dimensional systems.
  PhD thesis, University of Groningen, 2006. 
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• Mark R. Opmeer
  Discrete-time LQG-balancing in infinite dimensions.
  Master thesis, University of Groningen, 2002.