Sliding Mode Control for a Class of Linear Infinite-Dimensional Systems

This article deals with the stabilization of a class of linear infinite-dimensional systems with unbounded control operators and subject to a boundary disturbance. We assume that there exists a linear feedback law that makes the origin of the closed-loop system globally asymptotically stable in the...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 70; no. 5; pp. 3464 - 3470
Main Authors Balogoun, Ismaila, Marx, Swann, Plestan, Franck
Format Journal Article
LanguageEnglish
Published New York IEEE 01.05.2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Abstract control systems
Aerospace electronics
Asymptotic stability
Closed loop systems
Closed loops
Control systems
Convergence
Eigenvalues and eigenfunctions
Feedback control
Feedback control systems
Manifolds
Regulation
sliding mode
Sliding mode control
stabilization
Trajectory
Vectors
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Summary:This article deals with the stabilization of a class of linear infinite-dimensional systems with unbounded control operators and subject to a boundary disturbance. We assume that there exists a linear feedback law that makes the origin of the closed-loop system globally asymptotically stable in the absence of disturbance. To achieve our objective, we follow a sliding mode strategy, and we add another term to this controller in order to reject the disturbance. We prove the existence of solutions to the closed-loop system and its global asymptotic stability, while making sure the disturbance is rejected.
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content type line 14
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2025.3529282