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October 19, 20250 citationsOpen Access

Boundary Feedback and Observer Synthesis for a Class of Nonlinear Parabolic--Elliptic PDE Systems

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KFKamal FenzaMLMoussa LabbadiMOMohamed Ouzahra

Key Points

  • Exponential stability of the nonlinear closed-loop system is achieved through rigorous backstepping design, ensuring well-posedness.
  • An explicit boundary control law is provided based on partial boundary measurements, facilitating effective stabilization.
  • The integration of observers enables the system to converge exponentially, enhancing the overall system response.
  • The theorems established serve as a robust foundation for understanding the interplay between parabolic and elliptic PDE dynamics.

Abstract

This paper investigates the stabilization of a coupled system comprising a parabolic PDE and an elliptic PDE with nonlinear terms. A rigorous backstepping design provides an explicit boundary control law and exponentially convergent observers from partial boundary measurements. Several theorems ensure exponential stability and well-posedness of the nonlinear closed-loop system.

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Cite This Study

Fenza et al. (2025) studied this question.

synapsesocial.com/papers/68f4b10d3d9d770bbc696f5ahttps://doi.org/10.48550/arxiv.2507.12615
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