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

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DOI: https://doi.org/10.28924/2291-8639-21-2023-54
Published: Jun 16, 2023
Cite as:
Nor El-Houda Beghersa, Mehdi Benabdallah, Mohamed Hariri, On the Exponential Stability of the Implicit Differential Systems in Hilbert Spaces, Int. J. Anal. Appl., 21 (2023), 54.

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Nor El-Houda Beghersa, Mehdi Benabdallah, Mohamed Hariri

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.

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