\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Exponential stabilization of a linear Korteweg-de Vries equation with input saturation

  • * Corresponding author: Ahmat Mahamat Taboye

    * Corresponding author: Ahmat Mahamat Taboye 

Dedicated to Professor Mohammed Elarbi Achhab on the occasion of his retirement

Abstract Full Text(HTML) Related Papers Cited by
  • This article deals with the issue of the exponential stability of a linear Korteweg-de Vries equation with input saturation. It is proved that the system is well-posed and the origin is exponentially stable for the closed loop system, by using the classical argument used in this kind of problems.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
  • [1] E. Cerpa, Control of a korteweg-de Vries equation: A tutorial, Math. Control Relat. Fields, 4 (2014), 45-99.  doi: 10.3934/mcrf.2014.4.45.
    [2] E. Cerpa and J-M. Coron, Rapid stabilization for a Korteweg-de Vries equation from the left Dirichlet boundary condition, IEEE Trans. Automat. Control, 58 (2013), 1688-1695.  doi: 10.1109/TAC.2013.2241479.
    [3] J-M. Coron, Control and Nonlinearity, Mathematical Surveys and Monographs, 136, American Mathematical Society, Providence, RI, 2007. doi: 10.1090/surv/136.
    [4] R. F. Curtain and H. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory, Texts in Applied Mathematics, 21. Springer-Verlag, New York, 1995.
    [5] H. Hedenmalm, On the uniqueness theorem of Holmgren, Math. Z., 281 (2015), 357-378.  doi: 10.1007/s00209-015-1488-6.
    [6] K. Ito and F. Kappel, Evolution Equations and Approximations, World Scientific, 2002.
    [7] M. Laabissi and A. M. Taboye, Strong stabilization of non-dissipative operators in Hilbert spaces with input saturation, Math. Control Signals Systems, 33 (2021), 553-568.  doi: 10.1007/s00498-021-00291-1.
    [8] I. Lasiecka and T. I. Seidman, Strong stability of elastic control systems with dissipative saturating feedback, Systems Control Lett., 48 (2003), 243-252.  doi: 10.1016/S0167-6911(02)00269-4.
    [9] S. Marx and E. Cerpa, Output feedback control of the linear korteweg-de vries equation, IEEE Conference on Decision and Control, (2014), 2083–2087.
    [10] S. Marx, E. Cerpa, C. Prieur and V. Andrieu, Stabilization of a linear korteweg-de vries equation with a saturated internal control, In 2015 European Control Conference (ECC), IEEE, (2015), 867–872.
    [11] S. MarxE. CerpaC. Prieur and V. Andrieu, Global stabilization of a Korteweg–de Vries equation with saturating distributed control, SIAM J. Control Optim., 55 (2017), 1452-1480.  doi: 10.1137/16M1061837.
    [12] G. P. MenzalaC. F. Vasconcellos and E. Zuazua, Stabilization of the Korteweg-de Vries equation with localized damping, Quart. Appl. Math., 60 (2002), 111-129.  doi: 10.1090/qam/1878262.
    [13] I. Miyadera, Nonlinear Semigroups, American Mathematical Soc., 1992.
    [14] A. F. Pazoto, Unique continuation and decay for the Korteweg-de Vries equation with localized damping, ESAIM Control Optim. Calc. Var., 11 (2005), 473-486.  doi: 10.1051/cocv:2005015.
    [15] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
    [16] L. Rosier, Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain, ESAIM Control Optim. Calc. Var., 2 (1997), 33-55.  doi: 10.1051/cocv:1997102.
    [17] L. Rosier and B-Y. Zhang, Global stabilization of the generalized Korteweg–de Vries equation posed on a finite domain, SIAM J. Control Optim., 45 (2006), 927-956.  doi: 10.1137/050631409.
    [18] T. I. Seidman and H. Li, A note on stabilization with saturating feedback, Discrete Contin. Dynam. Systems, 7 (2001), 319-328.  doi: 10.3934/dcds.2001.7.319.
    [19] R. E. Showalter, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, American Mathematical Soc., Providence, RI, 1997.
    [20] M. Slemrod, Feedback stabilization of a linear control system in Hilbert space with an a priori bounded control, Math. Control Signals Systems, 2 (1989), 265-285.  doi: 10.1007/BF02551387.
    [21] B.-Y. Zhang, Exact boundary controllability of the Korteweg–de Vries equation, SIAM J. Control Optim., 37 (1999), 543-565.  doi: 10.1137/S0363012997327501.
  • 加载中
SHARE

Article Metrics

HTML views(517) PDF downloads(474) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return