Exponential stabilization with practical convergence of nonautonomous infinite-dimensional evolution equations

Authors

  • Hanen Damak Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, Stability and Control of Systems and PDEs Laboratory, Tunisia
  • Mohamed Ali Hammami Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, Tunisia

DOI:

https://doi.org/10.3842/umzh.v77i5.8393

Keywords:

Evolution operators. Feedback controller. Non-autonomous infinite-dimensional systems. Practical stabilization.

Abstract

UDC 517.9

We consider the asymptotic behaviors of solutions of certain differential equations in Banach spaces. It is proved that, under certain conditions with a restriction imposed on the perturbation term, certain classes of nonautonomous infinite-dimensional evolution equations can be almost feedback stabilized. We use integral inequalities and Lyapunov techniques to approach this problem. Moreover, we suggest some classes of memoryless state linear and nonlinear feedback controllers. To demonstrate the validity of the main result, an example is provided.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 77, No. 5, 2025.

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Published

04.07.2025

Issue

Vol. 77 No. 5 (2025)

Section

Research articles

License

Copyright (c) 2025 Hanen Damak, Mohamed Ali Hammami

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Damak, Hanen, and Mohamed Ali Hammami. “Exponential Stabilization With Practical Convergence of Nonautonomous Infinite-Dimensional Evolution Equations”. Ukrains’kyi Matematychnyi Zhurnal, vol. 77, no. 5, July 2025, p. 366, https://doi.org/10.3842/umzh.v77i5.8393.