Design of saturated controls for an unstable parabolic PDE

Abstract : 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 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. The efficiency of the proposed method is demonstrated by means of a numerical simulation.
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Submitted on : Monday, September 23, 2019 - 10:23:12 AM
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Andrii Mironchenko, Christophe Prieur, Fabian Wirth. Design of saturated controls for an unstable parabolic PDE. Joint 8th IFAC Symposium on Mechatronic Systems (MECHATRONICS'19) and 11th IFAC Symposium on Nonlinear Control Systems (NOLCOS'19), 2019, Vienna, Austria. ⟨hal-02294080⟩

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