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Boundary Stabilization of a Class of Coupled Hyperbolic‐Parabolic PDE Systems.

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Titel: Boundary Stabilization of a Class of Coupled Hyperbolic‐Parabolic PDE Systems.
Autoren: Guo, Qing1 (AUTHOR), Jin, Feng‐Fei1 (AUTHOR) jinfengfei@amss.ac.cn
Quelle: Mathematical Methods in the Applied Sciences. Dec2025, p1. 15p. 4 Illustrations.
Schlagwörter: *BACKSTEPPING control method, *EXPONENTIAL stability, *LYAPUNOV functions, *HYPERBOLIC differential equations, *STATE feedback (Feedback control systems), *DYNAMICAL systems
Abstract: ABSTRACT This paper considers the boundary state‐feedback stabilization problem of a novel hyperbolic‐parabolic coupled system, which exhibits not only boundary coupling but also complex internal coupling terms. By employing the backstepping method, the original system is transformed into a chosen target system, and two boundary feedback control laws are proposed. Exponential stability in the L2$$ {L}^2 $$ norm of the target system is established through the construction of an appropriate Lyapunov function. The effectiveness of the controller is demonstrated through a numerical simulation. [ABSTRACT FROM AUTHOR]
Datenbank: Academic Search Index
Beschreibung
Abstract:ABSTRACT This paper considers the boundary state‐feedback stabilization problem of a novel hyperbolic‐parabolic coupled system, which exhibits not only boundary coupling but also complex internal coupling terms. By employing the backstepping method, the original system is transformed into a chosen target system, and two boundary feedback control laws are proposed. Exponential stability in the L2$$ {L}^2 $$ norm of the target system is established through the construction of an appropriate Lyapunov function. The effectiveness of the controller is demonstrated through a numerical simulation. [ABSTRACT FROM AUTHOR]
ISSN:01704214
DOI:10.1002/mma.70385