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On hybrid dynamical systems of differential–difference equations

Author

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  • Dassios, Ioannis
  • Vaca, Angel
  • Milano, Federico

Abstract

In this paper, we define and study a class of linear hybrid dynamical systems characterized by differential–difference equations. We introduce two operators that facilitate the analysis of these systems and derive explicit formulas for their solutions. We examine the transfer function matrix and characteristic polynomial to assess stability. Our theoretical findings are supported by numerical examples, demonstrating their application in power systems stability analysis. Specifically, we substantiate our theory within the context of power systems stability analysis, incorporating elements of discrete behavior.

Suggested Citation

  • Dassios, Ioannis & Vaca, Angel & Milano, Federico, 2024. "On hybrid dynamical systems of differential–difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:chsofr:v:187:y:2024:i:c:s0960077924009834
    DOI: 10.1016/j.chaos.2024.115431
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