The paper is concerned with infinite-dimensional boundary control systems in Hilbert spaces. In order to handle controllability and stabilizability, the first part is devoted to transform equations of the initial boundary control system. Some necessary and sufficient conditions for exact controllability are proposed. In this case, the extended controllability Gramian is uniformly positive definite and bounded. This operator allows the authors to define a feedback control law which stabilizes exponentially the closed-loop system with an arbitrary decay rate. This feedback is defined from the inverse of the controllability Gramian.
Publié le : 2000-07-05
Classification:
boundary control systems,
stabilizability,
Exact controllability,
93D15, 93C25, 93B05,
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC],
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]
@article{hal-00830792,
author = {Dusser, Xavier and Rabah, Rabah},
title = {On exponential stabilizability for boundary control systems in Hilbert spaces},
journal = {HAL},
volume = {2000},
number = {0},
year = {2000},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00830792}
}
Dusser, Xavier; Rabah, Rabah. On exponential stabilizability for boundary control systems in Hilbert spaces. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-00830792/