On the Exponential Stability of the Implicit Differential Systems in Hilbert Spaces

Beghersa, Nor El-Houda; Benabdallah, Mehdi; Hariri, Mohamed

doi:10.28924/2291-8639-21-2023-54

Research Article

On the Exponential Stability of the Implicit Differential Systems in Hilbert Spaces

Nor El-Houda Beghersa*
Mehdi Benabdallah
Mohamed Hariri

* Corresponding author

Abstract

The aim of this research is to study the exponential stability of the stationary implicit system: Ax’(t) + Bx(t) = 0, where A and B are bounded operators in Hilbert spaces. The achieved results are the generalization of Liapounov Theorem for the spectrum of the operator pencil λA + B. We also establish the exponential stability conditions for the corresponding perturbed and quasi-linear implicit systems.

How to Cite

N. E.-H. Beghersa, M. Benabdallah, M. Hariri, On the Exponential Stability of the Implicit Differential Systems in Hilbert Spaces, Int. J. Anal. Appl. 21 (2023), 54. https://doi.org/10.28924/2291-8639-21-2023-54

BibTeX

@article{Beghersa2023,
  author  = {Beghersa, Nor El-Houda and Benabdallah, Mehdi and Hariri, Mohamed},
  title   = {On the Exponential Stability of the Implicit Differential Systems in Hilbert Spaces},
  journal = {Int. J. Anal. Appl.},
  volume  = {21},
  year    = {2023},
  pages   = {54},
  doi     = {10.28924/2291-8639-21-2023-54}
}

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