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Article Dans Une Revue IEEE Transactions on Automatic Control Année : 2021

Feedback Stabilization of a Class of Diagonal Infinite-Dimensional Systems with Delay Boundary Control

Hugo Lhachemi

Résumé

This article studies the boundary feedback stabilization of a class of diagonal infinite-dimensional boundary control systems. In the studied setting, the boundary control input is subject to a constant delay while the open-loop system might exhibit a finite number of unstable modes. The proposed control design strategy consists of two main steps. First, a finite-dimensional subsystem is obtained by truncation of the original infinite-dimensional system (IDS) via modal decomposition. It includes the unstable components of the IDS and allows the design of a finite-dimensional delay controller by means of the Artstein transformation and the pole-shifting theorem. Second, it is shown via the selection of an adequate Lyapunov function that: 1) the finite-dimensional delay controller successfully stabilizes the original IDS and 2) the closed-loop system is exponentially input-to-state stable (ISS) with respect to distributed disturbances. Finally, the obtained ISS property is used to derive a small gain condition ensuring the stability of an IDS-ODE interconnection.
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Dates et versions

hal-03093798 , version 1 (04-01-2021)

Identifiants

Citer

Hugo Lhachemi, Christophe Prieur. Feedback Stabilization of a Class of Diagonal Infinite-Dimensional Systems with Delay Boundary Control. IEEE Transactions on Automatic Control, 2021, 66 (1), pp.105-120. ⟨10.1109/TAC.2020.2975003⟩. ⟨hal-03093798⟩
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