Output stabilization of semilinear parabolic systems with bounded feedback

Abdessamad El Alami; Ali Boutoulout; Radouane Yafia

doi:10.31801/cfsuasmas.508205

Araştırma Makalesi

Output stabilization of semilinear parabolic systems with bounded feedback

Yıl 2019, Cilt: 68 Sayı: 1, 1114 - 1122, 01.02.2019

Abdessamad El Alami Ali Boutoulout Radouane Yafia

https://doi.org/10.31801/cfsuasmas.508205

Öz

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.

Anahtar Kelimeler

Output stabilzation, semilinear systems, bounded feedback

Kaynakça

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.

Yıl 2019, Cilt: 68 Sayı: 1, 1114 - 1122, 01.02.2019

Abdessamad El Alami Ali Boutoulout Radouane Yafia

https://doi.org/10.31801/cfsuasmas.508205

Öz

Kaynakça

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.

Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Bölüm	Makaleler
Yazarlar	Abdessamad El Alami 0000-0002-5251-6047 Ali Boutoulout 0000-0003-2545-1142 Radouane Yafia 0000-0002-9824-9036
Yayımlanma Tarihi	1 Şubat 2019
Gönderilme Tarihi	30 Mayıs 2018
Kabul Tarihi	30 Ağustos 2018
Yayımlandığı Sayı	Yıl 2019 Cilt: 68 Sayı: 1

Kaynak Göster

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. Şubat 2019;68(1):1114-1122. doi:10.31801/cfsuasmas.508205
Chicago	El Alami, Abdessamad, Ali Boutoulout, ve Radouane Yafia. “Output Stabilization of Semilinear Parabolic Systems With Bounded Feedback”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, sy. 1 (Şubat 2019): 1114-22. https://doi.org/10.31801/cfsuasmas.508205.
EndNote	El Alami A, Boutoulout A, Yafia R (01 Şubat 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, ve R. Yafia, “Output stabilization of semilinear parabolic systems with bounded feedback”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 68, sy. 1, ss. 1114–1122, 2019, doi: 10.31801/cfsuasmas.508205.
ISNAD	El Alami, Abdessamad vd. “Output Stabilization of Semilinear Parabolic Systems With Bounded Feedback”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (Şubat 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 vd. “Output Stabilization of Semilinear Parabolic Systems With Bounded Feedback”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 68, sy. 1, 2019, ss. 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.