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Stability analysis and model order reduction of coupled systems

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  • Timo Reis
  • Tatjana Stykel

Abstract

In this paper we discuss the stability and model order reduction of coupled linear time-invariant descriptor systems. Sufficient conditions for the asymptotic stability of a closed-loop system are given. We present a model reduction approach for coupled systems based on reducing the order of the subsystems and coupling the reduced-order models through the same interconnection relations as for the original system. Such an approach allows us to obtain error bounds for the reduced-order closed-loop system in terms of the errors in the reduced-order subsystems. Model reduction of coupled systems with unstable or improper subsystems is also considered. Numerical examples are given.

Suggested Citation

  • Timo Reis & Tatjana Stykel, 2007. "Stability analysis and model order reduction of coupled systems," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 13(5), pages 413-436, October.
    • Handle: RePEc:taf:nmcmxx:v:13:y:2007:i:5:p:413-436
    DOI: 10.1080/13873950701189071
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    Cited by:

    1. Karasözen, Bülent & Yıldız, Süleyman & Uzunca, Murat, 2022. "Intrusive and data-driven reduced order modelling of the rotating thermal shallow water equation," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    2. Bruno Dogančić & Marko Jokić & Neven Alujević & Hinko Wolf, 2022. "Structure Preserving Uncertainty Modelling and Robustness Analysis for Spatially Distributed Dissipative Dynamical Systems," Mathematics, MDPI, vol. 10(12), pages 1-31, June.
    3. Karasözen, Bülent & Mülayim, Gülden & Uzunca, Murat & Yıldız, Süleyman, 2021. "Reduced order modelling of nonlinear cross-diffusion systems," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    4. Uzunca, Murat & Karasözen, Bülent & Yıldız, Süleyman, 2021. "Structure-preserving reduced-order modeling of Korteweg–de Vries equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 193-211.

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