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Forwarding techniques for the global stabilization of dissipative infinite-dimensional systems coupled with an ODE

Abstract : This paper deals with the stabilization of a coupled system composed by an infinite-dimensional system and an ODE. Moreover, the control, which appears in the dynamics of the ODE, is subject to a general class of nonlinearities. Such a situation may arise, for instance, when the actuator admits a dynamics. The open-loop ODE is exponentially stable and the open-loop infinite-dimensional system is dissipative, i.e., the energy is nonincreasing, but its equilibrium point is not necessarily attractive. The feedback design is based on an extension of a finite-dimensional method, namely the forwarding method. We propose some sufficient conditions that imply the well-posedness and the global asymptotic stability of the closed-loop system. As illustration, we apply these results to a transport equation coupled with an ODE.
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https://hal.archives-ouvertes.fr/hal-02944073
Contributor : Swann Marx <>
Submitted on : Monday, September 21, 2020 - 10:50:20 AM
Last modification on : Monday, October 19, 2020 - 3:20:03 PM

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  • HAL Id : hal-02944073, version 1
  • ARXIV : 2009.10379

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Swann Marx, Lucas Brivadis, Daniele Astolfi. Forwarding techniques for the global stabilization of dissipative infinite-dimensional systems coupled with an ODE. 2020. ⟨hal-02944073⟩

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