发表机构
CRAN, CNRS, UMR 7039, University of Lorraine（洛林大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对时间退化抛物系统，通过算子相容性条件将退化演化方程正则化，结合临界-残差分解与有限到无限提升定理得到一致指数稳定性，最终导出构造性静态输出反馈综合方法，数值实验验证了相关结果。
AI 中文摘要
分布式参数系统的现代反馈设计预设闭环动力学定义了适定的演化问题，该预设对时间退化抛物系统而言并非平凡，时间退化不仅影响演化方程的分析性质，还会影响反馈互联的数学表述。研究表明，时间退化抛物系统的容许反馈互联可通过连接奇异反应算子与执行器和观测算子的算子相容性条件完全刻画，该刻画消除了闭环动力学的奇异分量，将退化演化方程约化为正则演化方程。基于该正则化表述，临界-残差分解得到一致指数稳定性证书，随后通过有限到无限提升定理将其推广至原无限维演化。最终，这些结果导出了构造性静态输出反馈综合方法。数值实验验证了正则化机制、稳定性证书及有限到无限提升的有效性。
英文摘要
Modern feedback design for distributed parameter systems presupposes that the closed-loop dynamics define a well-posed evolution problem. This presupposition becomes nontrivial for temporally degenerate parabolic systems, where temporal degeneracy affects not only the analytical properties of the evolution equation but also the mathematical formulation of the feedback interconnection itself. It is shown that admissible feedback interconnections for temporally degenerate parabolic systems are completely characterized by an operator compatibility condition linking the singular reaction operator with the actuator and observation operators. This characterization removes the singular component of the closed-loop dynamics and reduces the degenerate evolution equation to a regular evolution equation. Building upon this regularized formulation, a critical--residual decomposition yields a uniform exponential stability certificate, which is subsequently extended to the original infinite-dimensional evolution through a finite-to-infinite lifting theorem. A constructive static output feedback synthesis is finally obtained as a consequence of these results. Numerical experiments illustrate the regularization mechanism, validate the stability certificate, and confirm the finite-to-infinite lifting.
Comments44 pages, 6 figures
