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 59 articles )

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  1. Gosea, Ion Victor; Gugercin, Serkan: Data-driven modeling of linear dynamical systems with quadratic output in the AAA framework (2022)
  2. Gosea, Ion Victor; Gugercin, Serkan; Beattie, Christopher: Data-driven balancing of linear dynamical systems (2022)
  3. Ionescu, Tudor C.; Iftime, Orest V.; Necoara, Ion: Model reduction with pole-zero placement and high order moment matching (2022)
  4. Karasözen, Bülent; Yıldız, Süleyman; Uzunca, Murat: Intrusive and data-driven reduced order modelling of the rotating thermal shallow water equation (2022)
  5. Khodabakhshi, Parisa; Willcox, Karen E.: Non-intrusive data-driven model reduction for differential-algebraic equations derived from lifting transformations (2022)
  6. Sharma, Harsh; Wang, Zhu; Kramer, Boris: Hamiltonian operator inference: physics-preserving learning of reduced-order models for canonical Hamiltonian systems (2022)
  7. Benner, Peter; Goyal, Pawan: Interpolation-based model order reduction for polynomial systems (2021)
  8. Benner, Peter; Gugercin, Serkan; Werner, Steffen W. R.: Structure-preserving interpolation of bilinear control systems (2021)
  9. Benner, Peter; Gugercin, Serkan; Werner, Steffen W. R.: Structure-preserving interpolation for model reduction of parametric bilinear systems (2021)
  10. Brevis, Ignacio; Muga, Ignacio; van der Zee, Kristoffer G.: A machine-learning minimal-residual (ML-MRes) framework for goal-oriented finite element discretizations (2021)
  11. Gosea, Ion Victor; Güttel, Stefan: Algorithms for the rational approximation of matrix-valued functions (2021)
  12. Haasdonk, Bernard: MOR software (2021)
  13. Karachalios, Dimitrios S.; Gosea, Ion Victor; Antoulas, Athanasios C.: The Loewner framework for system identification and reduction (2021)
  14. Karachalios, D. S.; Gosea, I. V.; Antoulas, A. C.: On bilinear time-domain identification and reduction in the Loewner framework (2021)
  15. Khodkar, M. A.; Hassanzadeh, Pedram: A data-driven, physics-informed framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings (2021)
  16. Li, Yanpeng; Jiang, Yaolin; Yang, Ping: Time domain model order reduction of discrete-time bilinear systems with Charlier polynomials (2021)
  17. Nobile, Fabio; Pradovera, Davide: Non-intrusive double-greedy parametric model reduction by interpolation of frequency-domain rational surrogates (2021)
  18. Uy, Wayne Isaac Tan; Peherstorfer, Benjamin: Operator inference of non-Markovian terms for learning reduced models from partially observed state trajectories (2021)
  19. Uy, Wayne Isaac Tan; Peherstorfer, Benjamin: Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations (2021)
  20. Antoulas, Athanasios C.; Gosea, Ion Victor; Heinkenschloss, Matthias: Data-driven model reduction for a class of semi-explicit DAEs using the Loewner framework (2020)

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