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Approximate Controllability for a Class of Linear Neutral Evolution Systems with Infinite Delay

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Abstract

This paper deals with the approximate controllability problem for a class of linear neutral evolution systems with infinite delay in Banach spaces. Since the concerned system involves additional linear terms, the fundamental solution theory is used to describe the mild solutions. Based on the spectral analysis and the adjoint system, sufficient conditions for the approximate controllability of the concerned system are established. The rank condition is also shown when the control space is finite-dimensional. A practical example is given to show the application of the obtained results.

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Acknowledgements

We thank Professor Xianlong Fu from East China Normal University, Shanghai, China, for his comments that greatly improved the manuscript.

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  1. Laboratoire Systèmes Dynamiques et Applications, Université de Tlemcen (Abou bekr Belkaid University), Tlemcen, 13000, Algeria

    Fatima Zahra Mokkedem

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  1. Fatima Zahra Mokkedem
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Correspondence to Fatima Zahra Mokkedem.

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Mokkedem, F.Z. Approximate Controllability for a Class of Linear Neutral Evolution Systems with Infinite Delay. J Dyn Control Syst 28, 917–943 (2022). https://doi.org/10.1007/s10883-021-09560-3

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  • DOI: https://doi.org/10.1007/s10883-021-09560-3

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