Local stabilization of an unstable parabolic equation via saturated controls

@article{Mironchenko2019LocalSO,
  title={Local stabilization of an unstable parabolic equation via saturated controls},
  author={A. Mironchenko and C. Prieur and F. Wirth},
  journal={arXiv: Optimization and Control},
  year={2019}
}
  • A. Mironchenko, C. Prieur, F. Wirth
  • Published 2019
  • Mathematics
  • arXiv: Optimization and Control
  • 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… CONTINUE READING

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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 44 REFERENCES
    Design of saturated controls for an unstable parabolic PDE
    • 2
    • PDF
    ISS-Lyapunov functions for time-varying hyperbolic systems of balance laws
    • 109
    • PDF
    Cone-bounded feedback laws for m-dissipative operators on Hilbert spaces
    • 14
    • PDF
    Global Stabilization of a Korteweg-De Vries Equation With Saturating Distributed Control
    • 25
    • PDF
    Global stabilization and restricted tracking for multiple integrators with bounded controls
    • 864
    • PDF
    Feedback Stabilization of a 1-D Linear Reaction–Diffusion Equation With Delay Boundary Control
    • 31
    • PDF
    Feedback stabilization of a linear control system in Hilbert space with ana priori bounded control
    • 110
    Antiwindup design with guaranteed regions of stability: an LMI-based approach
    • 454
    • PDF