Delayed control-based controllability of discrete fractional higher-order neural networks

Weiyuan Ma, Chenjun Ma, Xiaoqin Wang and Weigang Sun

Chaos, Solitons & Fractals, 2025, vol. 200, issue P1

Abstract: This paper focuses on the controllability issues of discrete fractional higher-order neural networks with delayed control mechanisms. The matrix representation of the discrete Mittag-Leffler function is defined, and several fundamental properties are established using the discrete Laplace transform. It is revealed that the discrete fractional linear system is controllable if and only if the controllability Gramian matrix is nonsingular. Building on this foundation, a delayed control scheme is developed for discrete fractional higher-order neural networks, employing Schauder’s Fixed Point Theorem alongside the Gramian matrix. Finally, the effectiveness and practicality of the proposed methodologies are validated through three illustrative examples.

Keywords: Controllability; Gramian matrix; Delayed control; Neural networks; Higher-order interaction (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:200:y:2025:i:p1:s0960077925009464

DOI: 10.1016/j.chaos.2025.116933

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