The Loewner framework and transfer functions of singular/rectangular systems. A connection is established between the Loewner framework for model reduction and the generalized inverses of singular and rectangular matrices. In this context both the Moore-Penrose and the Drazin inverses are involved. As a consequence this approach yields transfer functions for singular and rectangular systems. Thus the Loewner framework constitutes a natural and direct way for constructing models from measured input/output data.

References in zbMATH (referenced in 51 articles )

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  1. Nakatsukasa, Yuji; Trefethen, Lloyd N.: An algorithm for real and complex rational minimax approximation (2020)
  2. Peherstorfer, Benjamin: Sampling low-dimensional Markovian dynamics for preasymptotically recovering reduced models from data with operator inference (2020)
  3. Pradovera, Davide: Interpolatory rational model order reduction of parametric problems lacking uniform inf-sup stability (2020)
  4. Regazzoni, F.; Dedè, L.; Quarteroni, A.: Machine learning of multiscale active force generation models for the efficient simulation of cardiac electromechanics (2020)
  5. Scarciotti, Giordano; Jiang, Zhong-Ping; Astolfi, Alessandro: Data-driven constrained optimal model reduction (2020)
  6. Rapisarda, P.: Discrete Roesser state models from 2D frequency data (2019)
  7. Regazzoni, F.; Dedè, L.; Quarteroni, A.: Machine learning for fast and reliable solution of time-dependent differential equations (2019)
  8. Carracedo Rodriguez, Andrea; Gugercin, Serkan; Borggaard, Jeff: Interpolatory model reduction of parameterized bilinear dynamical systems (2018)
  9. Gosea, I. V.; Petreczky, M.; Antoulas, A. C.: Data-driven model order reduction of linear switched systems in the Loewner framework (2018)
  10. Schulze, Philipp; Unger, Benjamin; Beattie, Christopher; Gugercin, Serkan: Data-driven structured realization (2018)
  11. Demourant, F.; Poussot-Vassal, C.: A new frequency-domain subspace algorithm with restricted poles location through LMI regions and its application to a wind tunnel test (2017)
  12. Kramer, Boris; Peherstorfer, Benjamin; Willcox, Karen: Feedback control for systems with uncertain parameters using online-adaptive reduced models (2017)
  13. Peherstorfer, Benjamin; Gugercin, Serkan; Willcox, Karen: Data-driven reduced model construction with time-domain Loewner models (2017)
  14. Uzunca, Murat; Karasözen, Bülent: Energy stable model order reduction for the Allen-Cahn equation (2017)
  15. Antoulas, A. C.: The Loewner framework and transfer functions of singular/rectangular systems (2016)
  16. Antoulas, A. C.; Gosea, I. V.; Ionita, A. C.: Model reduction of bilinear systems in the Loewner framework (2016)
  17. Benner, Peter; Goyal, Pawan: Multipoint interpolation of Volterra series and (\mathcalH_2)-model reduction for a family of bilinear descriptor systems (2016)
  18. Peherstorfer, Benjamin; Cui, Tiangang; Marzouk, Youssef; Willcox, Karen: Multifidelity importance sampling (2016)
  19. Peherstorfer, Benjamin; Willcox, Karen: Data-driven operator inference for nonintrusive projection-based model reduction (2016)
  20. Rapisarda, P.; Antoulas, A. C.: State-space modeling of two-dimensional vector-exponential trajectories (2016)