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On the Output Stabilization for a Class of Infinite Dimensional Bilinear Systems

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Recent Advances in Modeling, Analysis and Systems Control: Theoretical Aspects and Applications

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 243))

Abstract

This paper is concerned with the output stabilization for a class of distributed bilinear system evolving in a spatial domain \(\varOmega \). We give sufficient conditions for strong and weak output stabilization. Also, the question of the output stabilization is discussed using a minimization problem. Examples and simulations are given.

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References

  1. Ball, J.M., Slemrod, M.: Feedback stabilization of distributed semilinear control systems. J. Appl. Math. Optim. 5, 169–179 (1979)

    Article  MathSciNet  Google Scholar 

  2. Berrahmoune, L.: Stabilization and decay estimate for distributed bilinear systems. Syst. Control Lett. 36, 167–171 (2009)

    Article  MathSciNet  Google Scholar 

  3. Bounit, H., Hammouri, H.: Feedback stabilization for a class of distributed semilinear control systems. J. Nolinear Anal. Theory Method Appl. 37(8), 953–969 (1999)

    Article  MathSciNet  Google Scholar 

  4. Lasiecka, I., Tatau, D.: Uniform boundary stabilisation of semilinear wave equation with nonlinear boundary damping. Differ. Integr. Equ. 6 (1993)

    Google Scholar 

  5. Ouzahra, M.: Partial stabilisation of semilinear systems using bounded controls. Int. J. Control. 86(12), 2253–2262 (2013)

    Article  MathSciNet  Google Scholar 

  6. Pazy, A.: Semi-Groups of Linear Operators and Applications to Partial Differential Equations. Springer, New York (1983)

    Google Scholar 

  7. Zerrik, E., Ait Aadi, A., Larhrissi, R.: On the output feedback stabilization for distributed semilinear systems. Asian J. Control. https://doi.org/10.1002/asjc.2081

  8. Zerrik, E., Ait Aadi, A., Larhrissi, R.: Regional stabilization for a class of bilinear systems. IFAC-PapersOnLine, 50(1), 4540–4545 (2017)

    Article  Google Scholar 

  9. Zerrik, E., Ait Aadi, A., Larhrissi, R.: On the stabilization for a class of infinite dimensional bilinear systems with unbounded control operator. J. Nonlinear Dyn. Syst. Theory 18(4), 418–425 (2018)

    Google Scholar 

  10. Zerrik, E., Ouzahra, M.: Regional stabilization for infinite-dimensional systems. Int. J. Control. 76, 73–81 (2003)

    Article  MathSciNet  Google Scholar 

  11. Zerrik, E., Ouzahra, M., Ztot, K.: Regional stabilization for infinite bilinear systems. IEE Control Theory Appl. 151(1), 109–116 (2004)

    Article  Google Scholar 

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Acknowledgements

The work has been carried out with a grant from Hassan II Academy of Sciences and Technology.

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Correspondence to Abderrahman Ait Aadi .

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Zerrik, E.H., Aadi, A.A. (2020). On the Output Stabilization for a Class of Infinite Dimensional Bilinear Systems. In: Zerrik, E., Melliani, S., Castillo, O. (eds) Recent Advances in Modeling, Analysis and Systems Control: Theoretical Aspects and Applications. Studies in Systems, Decision and Control, vol 243. Springer, Cham. https://doi.org/10.1007/978-3-030-26149-8_14

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