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Stability Criterion of a Class of Non-causal Systems of Differential Equations

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Abstract

In this paper, we focus on a class of non-causal systems of differential equations, namely systems the variables of which can depend not only from the current or past time, but also from future time. For this type of systems, we study their solutions and present new and easily testable conditions under which any state of the system is stable. The stability analysis of a future-state-dependent set of differential equations has its relevance also in practical applications. Numerical examples, as well as an application in electric power engineering, are provided to justify our theory.

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Notes

  1. per unit system (pu); in power engineering, quantities are often expressed as fractions of defined base units.

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Acknowledgements

This work was supported by Sustainable Energy Authority of Ireland (SEAI), by funding Ioannis Dassios, and Federico Milano under Grant No. RDD/00681; and by the Swiss National Science Foundation, by funding Georgios Tzounas under NCCR Automation (grant no. 51NF40 18054).

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Authors and Affiliations

  1. FRESLIPS, University College Dublin, Dublin, Ireland

    Ioannis Dassios & Federico Milano

  2. ETH Zürich, Zürich, Switzerland

    Georgios Tzounas

Authors
  1. Ioannis Dassios
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  2. Georgios Tzounas
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  3. Federico Milano
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Correspondence to Ioannis Dassios.

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Dassios, I., Tzounas, G. & Milano, F. Stability Criterion of a Class of Non-causal Systems of Differential Equations. Circuits Syst Signal Process 42, 2452–2467 (2023). https://doi.org/10.1007/s00034-022-02221-1

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