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Article Dans Une Revue Mathematics of Control, Signals, and Systems Année : 2021

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

Résumé

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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Dates et versions

hal-02944073 , version 1 (21-09-2020)
hal-02944073 , version 2 (07-04-2021)

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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. Mathematics of Control, Signals, and Systems, 2021, 33. ⟨hal-02944073v2⟩
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