Skip to main content
SpringerLink
Log in

Output stabilization of distributed bilinear systems

  • Published:
Control Theory and Technology Aims and scope Submit manuscript

Abstract

This paper studies regional stabilization of a distributed bilinear system evolving on a spatial domain Ω. Sufficient conditions for regional weak, strong and exponential stabilization are given. Also we discuss a regional optimal stabilization problem. The obtained results are illustrated by examples and simulations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P. M. Pardalos, V. A. Yatsenko. Optimization and Control of Bilinear Systems Theory, Algorithms, and Applications. Boston: Springer, 2010.

    MATH  Google Scholar 

  2. M. Ouzhra. Exponential and weak stabilization of constrained bilinear systems. SIAM Journal on Control and Optimization, 2010, 48(6): 3962–3974.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. M. Ball, M. Slemrod. Feedback stabilization of distributed semilinear control systems. Applied Mathematics and Optimization, 1979, 5(1): 169–179.

    Article  MathSciNet  MATH  Google Scholar 

  4. L. Berrahmoune. Stabilization and decay estimate for distributed bilinear systems. Systems and control letters, 1999, 36(3): 167–171.

    Article  MathSciNet  MATH  Google Scholar 

  5. H. Bounit, H. Hammouri. Feedback stabilization for a class of distributed semilinear control systems. Nonlinear Analysis: Theory, Methods and Applications, 1999, 37(8): 953–969.

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Ouzhra. Feedback stabilization of parabolic systems with bilinear controls. Electronic Journal of Diferrential Equations, 2011, 38: 1–10.

    Google Scholar 

  7. E. Zerrik, A. El Jai. Stabilité des Systèmes Dynamiques. Perpignan: Presses Universitaires de Perpignan, 2014.

    Google Scholar 

  8. E. Zerrik, L. Ezzaki. Regional gradient stabilization of semilinear distributed systems. Journal of Dynamical and Control Systems, 2016, 23(2): 405–420.

    Article  MathSciNet  MATH  Google Scholar 

  9. E. Zerrik, M. Ouzahra, K. Ztot. Regional stabilization for infinite bilinear systems. IET Control Theory and Applications, 2004, 151(1): 109–116.

    Article  Google Scholar 

  10. A. Pazy. Semigroups of Linear Operations to Partial Differential Equations. New York: Springer, 1983.

    Book  MATH  Google Scholar 

  11. T. Penzl. Numerical solution of generalized Lyapunov equations. Advances in Computational Mathematics, 1998, 8(1): 33–48.

    Article  MathSciNet  MATH  Google Scholar 

  12. R. D. Skeel, M. Berzins. A method for the spatial discretization of parabolic equations in one space variable. SIAM Journal on Scientific and Statistical Computing, 1990, 11(1): 1–32.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. MACS Laboratory, Faculty of Sciences, Moulay Ismail University, Meknes, 50000, Morocco

    El Hassan Zerrik & Lahcen Ezzaki

Authors
  1. El Hassan Zerrik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lahcen Ezzaki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to El Hassan Zerrik.

Additional information

The work was supported by a grant from Hassan II Academy of Sciences and Technology.

El Hassan ZERRIK is a professor at Moulay Ismail University, Meknes, Morocco. He got his Ph.D. degree in Systems Theory (1993) at Mohammed V University, Rabat, Morocco. Professor Zerrik wrote many papers and books in the area of regional analysis of distributed systems. Currently, he is the head of the research team MACS (Modelling Analysis and Control of Systems) at Moulay Ismail University, Meknes, Morocco. E-mail: Zerrik3@yahoo.fr.

Lahcen EZZAKI is a researcher, pursuing his Ph.D. degree in Systems Theory at Moulay Ismail University, Meknes, Morocco. His research area is focused on regional stabilization of distributed systems. E-mail: ezzaki.lahcen@yahoo.fr.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zerrik, E., Ezzaki, L. Output stabilization of distributed bilinear systems. Control Theory Technol. 16, 58–71 (2018). https://doi.org/10.1007/s11768-018-6112-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11768-018-6112-y

Keywords

Search

Navigation