On the Stabilization for a Class of Distributed Bilinear Systems using Bounded Controls
Year 2019,
Volume: 1 Issue: 1, 28 - 40, 15.06.2019
El Hassan Zerrik
,
Abderrahman Ait Aadi
Abstract
This paper considers the question of the output stabilization for a class of infinite dimensional bilinear system evolving on a spatial domain $\Omega$. Then, we give sufficient conditions for exponential, strong and weak stabilization of the output of such systems. Examples and simualtions illustrate the efficiency of such controls.
References
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Automatica. 87 (2018) 210-217.
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Springer Verlag, New York (1983).
- [9] E. Zerrik, A. Ait Aadi and R. Larhrissi, Regional stabilization for a class of bilinear systems,
IFAC-PapersOnLine. 50 (2017) 4540-4545.
- [10] E. Zerrik, A. Ait Aadi and R. Larhrissi, On the stabilization of innite dimensional bilin-
ear systems with unbounded control operator, Journal of Nonlinear Dynamics and Systems
Theory. 18 (2018) 418-425.
- [11] E. Zerrik, A. Ait Aadi and R. Larhrissi, On the output feedback stabilization for distributed
semilinear systems, Asian Journal of Control. (2019) doi: 10.1002/asjc.2081.
- [12] E. Zerrik and M. Ouzahra, Regional stabilization for innite-dimensional systems, Interna-
tional Journal of Control. 76 (2003) 73-81.
- [13] E. Zerrik, M. Ouzahra and K. Ztot, Regional stabilization for innite bilinear systems, IET
Proceeding of Control Theory and Applications. 151 (2004) 109-116.
- [14] H. C. Zhou and G. Weiss, Output feedback exponential stabilization for one-dimensional un-
stable wave equations with boundary control matched disturbance, SIAM Journal on Control
and Optimization. 56 (2018) 4098-4129.
Year 2019,
Volume: 1 Issue: 1, 28 - 40, 15.06.2019
El Hassan Zerrik
,
Abderrahman Ait Aadi
References
- [1] J. M. Ball and M. Slemrod, Feedback stabilization of distributed semilinear control systems,
Journal of Applied Mathematics and Optimization. 5 (1979) 169-179.
- [2] L. Berrahmoune, Stabilization and decay estimate for distributed bilinear systems, Systems
Control Letters. 36 (1999) 167-171.
- [3] H. Bounit and H. Hammouri, Feedback stabilization for a class of distributed semilinear
control systems, Nonlinear Analysis. 37 (1999) 953-969.
- [4] W. Guo, Y. Chen and H. Feng, Output feedback stabilization for a Kirchhoff-type nonlinear
beam with general corrupted boundary observation, International Journal of Robust and
Nonlinear Control. (2017) doi: 10.1002/rnc.3740.
- [5] I. Lasiecka and D. Tataru, Uniform boundary stabilisation of semilinear wave equation with
nonlinear boundary damping, Journal of Difierential and Integral Equations. 6 (1993) 507-
533.
- [6] S. Marx and E. Cerpa, Output feedback stabilization of the Korteweg-de Vries equation,
Automatica. 87 (2018) 210-217.
- [7] M. Ouzahra, Partial stabilization of semilinear systems using bounded controls, Interna-
tional Journal of Control. 86 (2013) 2253-2262.
- [8] A. Pazy, Semi-groups of linear operators and applications to partial differential equations,
Springer Verlag, New York (1983).
- [9] E. Zerrik, A. Ait Aadi and R. Larhrissi, Regional stabilization for a class of bilinear systems,
IFAC-PapersOnLine. 50 (2017) 4540-4545.
- [10] E. Zerrik, A. Ait Aadi and R. Larhrissi, On the stabilization of innite dimensional bilin-
ear systems with unbounded control operator, Journal of Nonlinear Dynamics and Systems
Theory. 18 (2018) 418-425.
- [11] E. Zerrik, A. Ait Aadi and R. Larhrissi, On the output feedback stabilization for distributed
semilinear systems, Asian Journal of Control. (2019) doi: 10.1002/asjc.2081.
- [12] E. Zerrik and M. Ouzahra, Regional stabilization for innite-dimensional systems, Interna-
tional Journal of Control. 76 (2003) 73-81.
- [13] E. Zerrik, M. Ouzahra and K. Ztot, Regional stabilization for innite bilinear systems, IET
Proceeding of Control Theory and Applications. 151 (2004) 109-116.
- [14] H. C. Zhou and G. Weiss, Output feedback exponential stabilization for one-dimensional un-
stable wave equations with boundary control matched disturbance, SIAM Journal on Control
and Optimization. 56 (2018) 4098-4129.