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Research Article

Sufficient and necessary conditions of exponential stabilisation for a class of distributed second-order semilinear systems with time delay

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Received 16 Sep 2023, Accepted 19 Feb 2024, Published online: 04 Mar 2024

References

  • Ammari, K., & Nicaise, S. (2015). Stabilization of second order evolution equations with unbounded feedback with Delay. In Stabilization of Elastic Systems by Collocated Feedback (pp. 61–71). Springer.
  • Datko, R. (1988). Not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks. SIAM Journal on Control and Optimization, 26(3), 697–713. https://doi.org/10.1137/0326040
  • Hamidi, Z., Ouzahra, M., & Elazzouzi, A. (2020). Strong stabilization of distributed bilinear systems with time delay. Journal of Dynamical and Control Systems, 26(2), 243–254. https://doi.org/10.1007/s10883-019-09459-0
  • Haraux, A. (1989). Une remarque sur la stabilisation de certains systèmes du deuxième ordre en temps. Portugaliae Mathematica, 46(3), 245–258.
  • Houch, A. E., Tsouli, A., Benslimane, Y., & Attioui, A. (2021). Feedback stabilisation and polynomial decay estimate for distributed bilinear parabolic systems with time delay. International Journal of Control, 94(6), 1693–1703. https://doi.org/10.1080/00207179.2019.1663370
  • Liénard, A. (1928). Etude des oscillations entretenues. Revue Générale de L'Electricité, 23, 901–912. and 946-954.
  • Nicaise, S., & Pignotti, C. (2006a). Stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks. SIAM Journal on Control and Optimization, 45(5), 1561–1585. https://doi.org/10.1137/060648891
  • Nicaise, S., & Pignotti, C. (2006b). Stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks. SIAM Journal on Control and Optimization, 45(5), 1561–1585. https://doi.org/10.1137/060648891
  • Nicaise, S., & Pignotti, C. (2012). Asymptotic stability of second-order evolution equations with intermittent delay. Advances in Differential Equations, 17(9/10), 879–902. https://doi.org/10.57262/ade/1355702926
  • Nicaise, S., & Pignotti, C. (2014). Stabilization of second-order evolution equations with time delay. Mathematics of Control, Signals, and Systems, 26(4), 563–588. https://doi.org/10.1007/s00498-014-0130-1
  • Ouarit, M., & Tsouli, A. (2022). Exponential stabilisation of delayed distributed semilinear systems in Banach spaces. International Journal of Control, 1–11. https://doi.org/10.1080/00207179.2022.2158946
  • Ouarit, M., & Tsouli, A. (2024). Feedback stabilization of non-homogeneous distributed bilinear systems with varying time delay. Journal of Mathematical Analysis and Applications, 531(2), 127852. https://doi.org/10.1016/j.jmaa.2023.127852
  • Privat, Y., Trélat, E., & Zuazua, E. (2013). Optimal location of controllers for the one-dimensional wave equation. Annales de L'Institut Henri Poincaré C, Analyse non Linéaire, 30(6), 1097–1126.
  • Tebou, L. T. (2009). Equivalence between observability and stabilization for a class of second order semilinear evolution. In Conference Publications (Vol. 2009, pp. 744).
  • Tsouli, A., Houch, A. E., Benslimane, Y., & Attioui, A. (2021). Feedback stabilisation and polynomial decay estimate for time delay bilinear systems. International Journal of Control, 94(8), 2065–2071. https://doi.org/10.1080/00207179.2019.1693061
  • Tsouli, A., & Ouarit, M. (2022). Uniform exponential stabilization of distributed bilinear parabolic time delay systems with bounded feedback control. Archives of Control Sciences, 32(2), 257–278.
  • Tsouli, A., & Ouarit, M. (2023). Strong stabilisation and decay estimate for distributed semilinear systems with time-varying delay. International Journal of Control, 1–11. https://doi.org/10.1080/00207179.2023.2182178
  • Wu, J. (1996). Theory and applications of partial functional differential equations. Springer Verlag Berlin.

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