We study the dynamic behavior and stability of two connected Rayleigh beams that are subject to, in addition to two sensors and two actuators applied at the joint point, one of the actuators also specially distributed along the beams. We show that with the distributed control employed, there is a set of generalized eigenfunctions of the closed-loop system, which forms a Riesz basis with parenthesis for the state space. Then both the spectrum-determined growth condition and exponential stability are concluded for the system. Moreover, we show that the exponential stability is independent of the location of the joint. The range of the feedback gains that guarantee the system to be exponentially stable is identified.
Classification : 93C20, 93C25, 35J10, 47E05
Mots clés : Rayleigh beam, collocated control, spectral analysis, exponential stability
@article{COCV_2008__14_3_632_0,
author = {Guo, Bao-Zhu and Wang, Jun-Min and Zhou, Cui-Lian},
title = {On the dynamic behavior and stability of controlled connected {Rayleigh} beams under pointwise output feedback},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {632--656},
publisher = {EDP-Sciences},
volume = {14},
number = {3},
year = {2008},
doi = {10.1051/cocv:2008001},
zbl = {1146.93026},
mrnumber = {2434070},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2008001/}
}
TY - JOUR AU - Guo, Bao-Zhu AU - Wang, Jun-Min AU - Zhou, Cui-Lian TI - On the dynamic behavior and stability of controlled connected Rayleigh beams under pointwise output feedback JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2008 DA - 2008/// SP - 632 EP - 656 VL - 14 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2008001/ UR - https://zbmath.org/?q=an%3A1146.93026 UR - https://www.ams.org/mathscinet-getitem?mr=2434070 UR - https://doi.org/10.1051/cocv:2008001 DO - 10.1051/cocv:2008001 LA - en ID - COCV_2008__14_3_632_0 ER -
Guo, Bao-Zhu; Wang, Jun-Min; Zhou, Cui-Lian. On the dynamic behavior and stability of controlled connected Rayleigh beams under pointwise output feedback. ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 3, pp. 632-656. doi : 10.1051/cocv:2008001. http://www.numdam.org/articles/10.1051/cocv:2008001/
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