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Output stabilization of semilinear parabolic systems with bounded feedback

Year 2019, Volume: 68 Issue: 1, 1114 - 1122, 01.02.2019
https://doi.org/10.31801/cfsuasmas.508205

Abstract

In this paper, we will study the output feedback stabilization of infinite-semilinear parabolic systems evolving on a spatial domain Ω and in a subregion ω of Ω (interior to Ω or on its boundary ∂Ω). We consider the condition of admissibility and the decomposition methods technique of the state space via the spectral properties of the system. Then we apply this approach to a regional exponential stabilization problem using bounded feedback. Applications are presented.

References

  • Tsouli, A., Boutoulout, A. and El Alami, A., Constrained Feedback Stabilization for Bilinear Parabolic Systems, Intelligent Control and Automation, 6, (2015), 103-115.
  • El Harraki, I., El Alami, A., Boutoulout, A. and Serhani, M., Regional stabilization for semilinear parabolic systems, IMA Journal of Mathematical Control and Information, (2016), 2015-197.
  • Zerrik, EL. and Ouzara, M., Output stabilization for infinite-dimentionel bilinear systems, Int. J. Appl. Math. Comput. Sci., Vol. 15, No. 2, (2005), 187-195.
  • Ball, J. and Slemrod, M., Feedback stabilization of distributed semilinear control systems, Appl. Math. Opt., 5, (1979), 169-179.
  • Kato, T., Perturbation theory for linear operators, New York., Springer, 1980.
  • Berrahmoune, L., Stabilization and decay estimate for distributed bilinear systems, Systems and Control Letters, 36 (1999), 167-171.
  • Berrahmoune, L., Stabilization of bilinear control systems in Hilbert space with nonquadratic feedback, Rend. Circ. Mat. Palermo, 58 (2009), 275-282.
  • Ouzahra, M., Stabilization of infinite-dimensional bilinear systems using a quadratic feedback control, International Journal of Control, 82 (2009), 1657-1664.
  • Ouzahra, M., Exponential and weak stabilization of constrained bilinear systems, SIAM J. Control Optim., 48, Issue 6 (2010), 3962-3974.
  • Pazy, A., Semi-groups of linear operators and applications to partial differential equations, Springer Verlag, New York, 1983.
  • Quinn, J. P., Stabilization of bilinear systems by quadratic feedback control, J. Math. Anal. Appl., 75 (1980), 66-80.
  • Weiss,G., Admissibility of unbounded control operators. SIAM J Control Optim., 27 (1989), 527-545.
Year 2019, Volume: 68 Issue: 1, 1114 - 1122, 01.02.2019
https://doi.org/10.31801/cfsuasmas.508205

Abstract

References

  • Tsouli, A., Boutoulout, A. and El Alami, A., Constrained Feedback Stabilization for Bilinear Parabolic Systems, Intelligent Control and Automation, 6, (2015), 103-115.
  • El Harraki, I., El Alami, A., Boutoulout, A. and Serhani, M., Regional stabilization for semilinear parabolic systems, IMA Journal of Mathematical Control and Information, (2016), 2015-197.
  • Zerrik, EL. and Ouzara, M., Output stabilization for infinite-dimentionel bilinear systems, Int. J. Appl. Math. Comput. Sci., Vol. 15, No. 2, (2005), 187-195.
  • Ball, J. and Slemrod, M., Feedback stabilization of distributed semilinear control systems, Appl. Math. Opt., 5, (1979), 169-179.
  • Kato, T., Perturbation theory for linear operators, New York., Springer, 1980.
  • Berrahmoune, L., Stabilization and decay estimate for distributed bilinear systems, Systems and Control Letters, 36 (1999), 167-171.
  • Berrahmoune, L., Stabilization of bilinear control systems in Hilbert space with nonquadratic feedback, Rend. Circ. Mat. Palermo, 58 (2009), 275-282.
  • Ouzahra, M., Stabilization of infinite-dimensional bilinear systems using a quadratic feedback control, International Journal of Control, 82 (2009), 1657-1664.
  • Ouzahra, M., Exponential and weak stabilization of constrained bilinear systems, SIAM J. Control Optim., 48, Issue 6 (2010), 3962-3974.
  • Pazy, A., Semi-groups of linear operators and applications to partial differential equations, Springer Verlag, New York, 1983.
  • Quinn, J. P., Stabilization of bilinear systems by quadratic feedback control, J. Math. Anal. Appl., 75 (1980), 66-80.
  • Weiss,G., Admissibility of unbounded control operators. SIAM J Control Optim., 27 (1989), 527-545.
There are 12 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

Abdessamad El Alami This is me 0000-0002-5251-6047

Ali Boutoulout This is me 0000-0003-2545-1142

Radouane Yafia This is me 0000-0002-9824-9036

Publication Date February 1, 2019
Submission Date May 30, 2018
Acceptance Date August 30, 2018
Published in Issue Year 2019 Volume: 68 Issue: 1

Cite

APA El Alami, A., Boutoulout, A., & Yafia, R. (2019). Output stabilization of semilinear parabolic systems with bounded feedback. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 1114-1122. https://doi.org/10.31801/cfsuasmas.508205
AMA El Alami A, Boutoulout A, Yafia R. Output stabilization of semilinear parabolic systems with bounded feedback. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2019;68(1):1114-1122. doi:10.31801/cfsuasmas.508205
Chicago El Alami, Abdessamad, Ali Boutoulout, and Radouane Yafia. “Output Stabilization of Semilinear Parabolic Systems With Bounded Feedback”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 1 (February 2019): 1114-22. https://doi.org/10.31801/cfsuasmas.508205.
EndNote El Alami A, Boutoulout A, Yafia R (February 1, 2019) Output stabilization of semilinear parabolic systems with bounded feedback. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 1114–1122.
IEEE A. El Alami, A. Boutoulout, and R. Yafia, “Output stabilization of semilinear parabolic systems with bounded feedback”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 1114–1122, 2019, doi: 10.31801/cfsuasmas.508205.
ISNAD El Alami, Abdessamad et al. “Output Stabilization of Semilinear Parabolic Systems With Bounded Feedback”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 2019), 1114-1122. https://doi.org/10.31801/cfsuasmas.508205.
JAMA El Alami A, Boutoulout A, Yafia R. Output stabilization of semilinear parabolic systems with bounded feedback. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1114–1122.
MLA El Alami, Abdessamad et al. “Output Stabilization of Semilinear Parabolic Systems With Bounded Feedback”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, 2019, pp. 1114-22, doi:10.31801/cfsuasmas.508205.
Vancouver El Alami A, Boutoulout A, Yafia R. Output stabilization of semilinear parabolic systems with bounded feedback. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):1114-22.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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