Model Reduction for Norm Approximation: An Application to Large-Scale Time-Delay Systems

  • Igor Pontes DuffEmail author
  • Pierre Vuillemin
  • Charles Poussot-Vassal
  • Corentin Briat
  • Cédric Seren
Part of the Advances in Delays and Dynamics book series (ADVSDD, volume 6)


The computation of \(\mathscr {H}_2\) and \(\mathscr {H}_{2,\varOmega }\) norms for LTI Time-Delay Systems (TDS) are important challenging problems for which several solutions have been provided in the literature. Several of these approaches, however, cannot be applied to systems of large dimension because of the inherent poor scalability of the methods, e.g., LMIs or Lyapunov-based approaches. When it comes to the computation of frequency-limited norms, the problem tends to be even more difficult. In this chapter, a computationally feasible solution using \(\mathscr {H}_2\) model reduction for TDS, based on the ideas provided in [3], is proposed. It is notably demonstrates on several examples that the proposed method is suitable for performing both accurate model reduction and norm estimation for large-scale TDS.


Model Reduction Modal Truncation Lambert Function Model Reduction Problem Optimal Model Reduction 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Igor Pontes Duff
    • 1
    Email author
  • Pierre Vuillemin
    • 1
  • Charles Poussot-Vassal
    • 1
  • Corentin Briat
    • 2
  • Cédric Seren
    • 1
  1. 1.Onera-French Aerospace LabToulouseFrance
  2. 2.Department of Biosystems Science and Engineering (D-BSSE)The Swiss Federal Institute of Technology–Zürich (ETH-Z)ZurichSwitzerland

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