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

Local stabilization of an unstable parabolic equation via saturated controls

Résumé

We derive a saturated feedback control, which locally stabilizes a linear reaction-diffusion equation. In contrast to most other works on this topic, we do not assume the Lyapunov stability of the uncontrolled system and consider general unstable systems. Using Lyapunov methods, we provide estimates for the region of attraction for the closed-loop system, given in terms of linear and bilinear matrix inequalities. We show that our results can be used with distributed as well as scalar boundary control, and with different types of saturations. The efficiency of the proposed method is demonstrated by means of numerical simulations.
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Dates et versions

hal-03276343 , version 1 (02-07-2021)

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Andrii Mironchenko, Christophe Prieur, Fabian Wirth. Local stabilization of an unstable parabolic equation via saturated controls. IEEE Transactions on Automatic Control, 2021, 66 (5), pp.2162-2176. ⟨10.1109/TAC.2020.3007733⟩. ⟨hal-03276343⟩
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