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Singular over-determined systems of linear differential equations

Author

Listed:
  • Dassios, Ioannis
  • Tzounas, Georgios
  • Liu, Muyang
  • Milano, Federico

Abstract

We study a class of singular over-determined systems of differential equations and firstly prove that there exist solutions under certain conditions. For the case of existence we provide closed formulas of solutions and based on the spectrum of the pencil of the system we study uniqueness of solutions. Then, we extend these results to higher order singular overdetermined systems. Finally, we use this type of systems to model electrical power systems and provide numerical examples.

Suggested Citation

  • Dassios, Ioannis & Tzounas, Georgios & Liu, Muyang & Milano, Federico, 2022. "Singular over-determined systems of linear differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 396-412.
    • Handle: RePEc:eee:matcom:v:197:y:2022:i:c:p:396-412
    DOI: 10.1016/j.matcom.2022.02.003
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    References listed on IDEAS

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    1. Dassios, Ioannis K. & Baleanu, Dumitru I., 2018. "Caputo and related fractional derivatives in singular systems," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 591-606.
    2. Dassios, Ioannis & Tzounas, Georgios & Milano, Federico, 2019. "The Möbius transform effect in singular systems of differential equations," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 338-353.
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