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October 19, 2025Open Access

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

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. (Wed,) studied this question.

synapsesocial.com/papers/68f4b10d3d9d770bbc696f5a https://doi.org/https://doi.org/10.48550/arxiv.2507.12615

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