Scholarlink

<p>This paper investigates the boundary output feedback stabilization problem for a class of hyperbolic–parabolic partial differential equations. The primary objective is to design a stabilizing controller based on an observer for this unstable coupled PDE system. The observer is constructed in the form of “copy of the plant plus output injection,” while the controller design is accomplished through the backstepping method. Using operator semigroup theory, we establish the well-posedness of the closed-loop system. Under appropriate measurable outputs, we demonstrate that the proposed control law ensures exponential stability of the closed-loop system in the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^{2}(0,1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mn>2</mn> </msup> <mrow> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>-norm sense. Finally, the effectiveness of the controller is illustrated through a illustrative numerical simulation.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Output feedback stabilization of a class of hyperbolic–parabolic coupled system

  • 期刊论文

  • 发表日期：

    2026年1月2日

查看全文
  • Qing Guo,
  • Feng-Fei Jin

摘要

This paper investigates the boundary output feedback stabilization problem for a class of hyperbolic–parabolic partial differential equations. The primary objective is to design a stabilizing controller based on an observer for this unstable coupled PDE system. The observer is constructed in the form of “copy of the plant plus output injection,” while the controller design is accomplished through the backstepping method. Using operator semigroup theory, we establish the well-posedness of the closed-loop system. Under appropriate measurable outputs, we demonstrate that the proposed control law ensures exponential stability of the closed-loop system in the \(L^{2}(0,1)\) L 2 ( 0 , 1 ) -norm sense. Finally, the effectiveness of the controller is illustrated through a illustrative numerical simulation.