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6 - A Note on the Asymptotic Stability of Wave-Type Equations with Switching Time-Delay

Published online by Cambridge University Press:  25 October 2017

Serge Nicaise
Affiliation:
University of Valenciennes and of Hainaut Cambrésis
Cristina Pignotti
Affiliation:
Department of Engineering and Computer Science and Mathematics
Kaïs Ammari
Affiliation:
Université de Monastir, Tunisia
Stéphane Gerbi
Affiliation:
Université Savoie Mont Blanc, France
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Summary

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Type
Chapter
Information
Evolution Equations
Long Time Behavior and Control
, pp. 137 - 150
Publisher: Cambridge University Press
Print publication year: 2017

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References

[1] K., Ammari, S., Nicaise, and C., Pignotti. Stabilization by switching time-delay. Asymptot. Anal., 83:263–83, (2013).Google Scholar
[2] R., Datko. Not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks. SIAM J. Control Optim., 26:697–713, (1988).Google Scholar
[3] R., Datko, J., Lagnese, and M. P., Polis. An example on the effect of time delays in boundary feedback stabilization of wave equations. SIAM J. Control Optim., 24:152–6, (1986).Google Scholar
[4] H. D., Fernández Sare. On the stability of Mindlin–Timoshenko plates. Quart. Appl. Math., 67:249–63, (2009).Google Scholar
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[6] A., Haraux, P., Martinez, and J., Vancostenoble. Asymptotic stability for intermittently controlled second-order evolution equations. SIAM J. Control Optim., 43:2089-108, (2005).Google Scholar
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[8] J.E., Lagnese, Boundary stabilization of thin plates, SIAM Studies in Applied Mathematics, 10, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, (1989).
[9] S., Nicaise and C., Pignotti. Stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks. SIAM J. Control Optim., 45:1561–85, (2006).Google Scholar
[10] S., Nicaise and C., Pignotti. Asymptotic stability of second-order evolution equations with intermittent delay. Adv. Diff. Eq., 17:879–902, (2012).Google Scholar
[11] S., Nicaise and C., Pignotti. Stability results for second-order evolution equations with switching time-delay. J. Dyn. Diff. Eq., 26:781–803, (2014).Google Scholar
[12] S., Nicaise. Internal stabilization of a Mindlin–Timoshenko model by interior feedbacks. Math. Control Relat. Fields, 1:331–52, (2011).Google Scholar
[13] C., Pignotti. A note on stabilization of locally damped wave equations with time delay. Systems Control Lett., 61:92–7, (2012).Google Scholar
[14] G.Q., Xu, S.P., Yung, and L. K., Li. Stabilization of wave systems with input delay in the boundary control. ESAIM: Control Optim. Calc. Var., 12:770–85, 2006.

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