Boundary feedback stabilization of conformablelinear systems
DOI: https://doi.org/10.3846/mma.2026.25053Abstract
In this paper, we study the stabilization of infinitedimensional boundary control systems governed by the conformable derivative of order α ∈ (0, 1]. To address this problem, we reformulate the boundary stabilization problem as that of an associated linear internal control system governed by the conformable derivative, thereby enabling the use of techniques originally developed for integer-order dynamics. A stabilizing feedback law is then designed by extending classical results on linear internal control systems to the conformable setting. Exponential stabilization is established, and strong stabilization is also obtained for a broad class of Rieszspectral boundary control systems. The effectiveness of the proposed approach is demonstrated through its application to the heat equation governed by the conformable derivative, supported by numerical simulations that confirm the theoretical findings.
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conformable derivative, stabilization, boundary control, Dirichlet operator, fractional semigroupsHow to Cite
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Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University.
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Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University.
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