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Cone-bounded feedback laws for m-dissipative operators on Hilbert spaces

Abstract : This work studies the influence of some constraints on a stabilizing feedback law. It is considered an abstract nonlinear control system for which we assume that there exists a linear feedback law that makes the origin of the closed-loop system globally asymptotically stable. This controller is then modified via a cone-bounded nonlinearity. A well-posedness and a stability theorems are stated. The first theorem is proved thanks to the Schauder fixed-point theorem, the second one with an infinite-dimensional version of LaSalle's Invariance Principle. These results are illustrated on a linear Korteweg-de Vries equation by some simulations and on a nonlinear heat equation.
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https://hal.archives-ouvertes.fr/hal-01620024
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Submitted on : Friday, October 20, 2017 - 9:36:19 AM
Last modification on : Thursday, August 4, 2022 - 5:13:58 PM
Long-term archiving on: : Sunday, January 21, 2018 - 12:53:05 PM

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Swann Marx, Vincent Andrieu, Christophe Prieur. Cone-bounded feedback laws for m-dissipative operators on Hilbert spaces. Mathematics of Control, Signals, and Systems, Springer Verlag, 2017, 29 (4), pp.18. ⟨10.1007/s00498-017-0205-x⟩. ⟨hal-01620024⟩

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