Skip to main content Accessibility help
×
Home
Hostname: page-component-55597f9d44-dfw9g Total loading time: 0.348 Render date: 2022-08-19T06:32:52.500Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

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
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Evolution Equations
Long Time Behavior and Control
, pp. 137 - 150
Publisher: Cambridge University Press
Print publication year: 2017

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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
[5] M., Gugat. Boundary feedback stabilization by time delay for one-dimensional wave equations. IMA J. Math. Control Inform., 27:189–203, (2010).Google Scholar
[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
[7] J., Lagnese and J.-L., Lions, Modelling analysis and control of thin plates, Recherches en Mathématiques Appliquées [Research in Applied Mathematics], 6, Masson, Paris, (1988).
[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.

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×