THE EFFECT OF SMALL TIME DELAYS IN THE FEEDBACKS ON BOUNDARY STABILIZATION

Authors
LI XJ LIU KS
Citation
Xj. Li et Ks. Liu, THE EFFECT OF SMALL TIME DELAYS IN THE FEEDBACKS ON BOUNDARY STABILIZATION, Science in China. Series A, Mathematics, Physics, Astronomy & Technological Sciences, 36(12), 1993, pp. 1435-1443
Citations number
15
Categorie Soggetti
Multidisciplinary Sciences
Journal title
Science in China. Series A, Mathematics, Physics, Astronomy & Technological Sciences → ACNP
ISSN journal
10016511
Volume
36
Issue
12
Year of publication
1993
Pages
1435 - 1443
Database
ISI
SICI code
1001-6511(1993)36:12<1435:TEOSTD>2.0.ZU;2-T
Abstract
In this paper we discuss the effect of small time delays in the feedba cks on stabilization. It is proved that with respect to small time del ays in the feedbacks, (boundary) stabilizations of parabolic systems a re robust, but symmetric stabilization of infinitely-dimensional conse rvative systems is not robust. For example, the current boundary stabi lization of the wave equation is not robust with respect to small time delays in its feedback. This is an answer to a problem posed in [1].