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Applicable Analysis
An International Journal
Volume 96, 2017 - Issue 15
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Original Articles

Exponential stability analysis of Timoshenko beam system with boundary delays

Zongfei TianDepartment of Mathematics, Tianjin University, Tianjin, P.R. China.View further author information
&
Gen-Qi XuDepartment of Mathematics, Tianjin University, Tianjin, P.R. China.Correspondence[email protected]
ORCID Iconhttp://orcid.org/0000-0001-8120-0490View further author information
ORCID Icon
Pages 2575-2603 | Received 26 Apr 2016, Accepted 26 Aug 2016, Published online: 14 Sep 2016

References

  • Timoshenko S. Vibration problems in engineering. New York (NY): Van Norstrand; 1955.
  • Abdallah C, Dorato P, Benitez-Read J, et al. Delayed positive feedback can stabilize oscillatory system. In: American Control Conference, ACC. San Francisco, CA; 1993. p. 3106–3107.
  • Suh IH, Bien Z. Use of time delay action in the controller design. IEEE Trans. Autom. Control. 1980;25:600–603.
  • Datko R, Lagnese J, Polis MP. An example on the effect of time delays in boundary feedback stabilization of wave equations. SIAM J. Control Optim. 1986;24:152–156.
  • Datko R. Two questions concerning the boundary control of certain elastic systems. J. Differ. Equ. 1991;92:27–44.
  • Datko R. Two examples of ill-posedness with respect to small time delays in stabilized elastic systems. IEEE Trans. Autom. Control. 1993;38:163–166.
  • Raposo CA, Ferreira J, Santos ML, et al. Exponential stability for the Timoshenko system with two weak dampings. Appl. Math. Lett. 2005;18:535–541.
  • Shi DH, Feng DX. Exponential decay of Timoshenko beam with locally distributed feedback. IMA J. Math. Control Inf. 2001;18:395–403.
  • Soufyane A. Stabilisation de la poutre de Timoshenko [Stabilization of Timoshenko beam]. C. R. Acad. Sci. Paris Ser. I Math. 1999;328:731–734.
  • Soufyane A, Wehbe A. Exponential stability for the Timoshenko beam by a locally distributed damping. Electron J. Differ. Equ. 2003;29:1–14.
  • Munoz Rivera JE, Racke R. Timoshenko systems with indefinite damping. J. Math. Anal. Appl. 2008;341:1068–1083.
  • Xu GQ, Yung SP. Stabilization of Timoshenko beam by means of pointwise controls. ESAIM: Control Optim. Calc. Var. 2003;9:579–600.
  • Kim JU, Renardy R. Boundary control of the Timoshenko beam. SIAM J. Control. Optim. 1987;25:1417–1429.
  • Han ZJ, Xu GQ. Exponential stability of Timoshenko beam system with delay terms in boundary feedbacks. ESAIM: Control Optim. Calc. Var. 2011;17:552–574.
  • Xu GQ, Wang HX. Stabilisation of Timoshenko beam system with delay in the boundary control. Int. J. Control. 2013;86:1165–1178.
  • Said-Houari B, Laskri Y. A stability result of a Timoshenko system with a delay term in the internal feedback. Math. Comput. 2010;217:2857–2869.
  • Kirane M, Said-Houari B, Anwar MN. Stability result for the Timoshenko system with a time-varying delay term in the internal feedbacks. Commun. Pure Appl. Anal. 2011;10:667–686.
  • Said-Houari B, Soufyane A. Stability result of the Timoshenko system with delay and boundary feedback. IMA J. Math. Control Inf. 2012;6:1–16.
  • Pazy A. Semigroups of linear operators and applications to partial differential equations. Berlin: Springer-Verlag; 1983.
  • Guo BZ, Jin FF. The active disturbance rejection and sliding mode control approach to the stabilization of the Euler--Bernoulli beam equation with boundary input disturbance. Automatica. 2013;49:2911–2918.
  • He W, Ge SS, How BVE, et al. Robust adaptive boundary control of a flexible marine riser with vessel dynamics. Automatica. 2011;47:722–732.
  • He W, Sun C, Ge SS. Top tension control of a flexible marine riser by using integral-barrier Lyapunov function. IEEE/ASME Trans. Mechatron. 2015;20:497–505.
  • He W, Ge SS. Vibration control of a flexible beam with output constraint. IEEE Trans. Ind. Electron. 2015;62:5023–5030.

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