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

  • Swann Marx
  • Vincent Andrieu
  • Christophe Prieur
Original Article

Abstract

This work studies the influence of some constraints on a stabilizing feedback law. An abstract nonlinear control system is considered 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. Well-posedness and stability theorems are stated. The first theorem is proved thanks to the Schauder fixed-point theorem and 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.

Keywords

Nonlinear semigroups Stabilization Abstract control systems 

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Copyright information

© Springer-Verlag London Ltd. 2017

Authors and Affiliations

  1. 1.Univ. Grenoble Alpes, CNRS, Gipsa-labGrenobleFrance
  2. 2.Université Lyon 1 CNRS UMR 5007 LAGEPLyonFrance

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