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Identification of Linear Time-Invariant Systems with Dynamic Mode Decomposition

Author

Listed:
  • Jan Heiland

    (Max Planck Institute for Dynamics of Complex Technical Systems, 39106 Magdeburg, Germany
    Current address: Faculty of Mathematics, Otto von Guericke University Magdeburg, 39106 Magdeburg, Germany.
    These authors contributed equally to this work.)

  • Benjamin Unger

    (Stuttgart Center for Simulation Science, University of Stuttgart, 70563 Stuttgart, Germany
    These authors contributed equally to this work.)

Abstract

Dynamic mode decomposition (DMD) is a popular data-driven framework to extract linear dynamics from complex high-dimensional systems. In this work, we study the system identification properties of DMD. We first show that DMD is invariant under linear transformations in the image of the data matrix. If, in addition, the data are constructed from a linear time-invariant system, then we prove that DMD can recover the original dynamics under mild conditions. If the linear dynamics are discretized with the Runge–Kutta method, then we further classify the error of the DMD approximation and detail that for one-stage Runge–Kutta methods; even the continuous dynamics can be recovered with DMD. A numerical example illustrates the theoretical findings.

Suggested Citation

  • Jan Heiland & Benjamin Unger, 2022. "Identification of Linear Time-Invariant Systems with Dynamic Mode Decomposition," Mathematics, MDPI, vol. 10(3), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:418-:d:736878
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