Abstract
We consider a pointwise stabilization problem for a model arising in the control of noise. We prove that we have exponential stability for the low frequencies but not for the high frequencies. Thus, we give an explicit polynomial decay estimation at high frequencies that is valid for regular initial data while clarifying that the behavior of the constant which intervenes in this estimation there, functions as the frequency of cut. We propose a numerical approximation of the model and study numerically the best location of the actuator at low frequencies.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Ammari, K., Saidi, A. Pointwise Stabilization of a Hybrid System and Optimal Location of Actuator. Appl Math Optim 56, 105–130 (2007). https://doi.org/10.1007/s00245-007-0881-x
Issue Date:
DOI: https://doi.org/10.1007/s00245-007-0881-x