Finite-time stability of fractional-order fuzzy inertial neural networks via a new finite-time inequality

Tiecheng Zhang; Wenxiang Fang; Liyan Wang; Yulong Lu; Tiecheng Zhang; Wenxiang Fang; Liyan Wang; Yulong Lu

doi:10.3934/math.2026245

AIMS Mathematics

2026, Volume 11, Issue 3: 5936-5953. doi: 10.3934/math.2026245

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Finite-time stability of fractional-order fuzzy inertial neural networks via a new finite-time inequality

1.
Huangshi Key Laboratory of Metaverse and Virtual Simulation, School of Mathematics and Statistics, Hubei Normal University, Huangshi, Hubei 435002, China
2.
School of Science, China University of Geosciences, Beijing 100084, China
3.
School of Automation, Hubei University of Science and Technology, Xianning, Hubei 437100, China

Received: 25 December 2025 Revised: 04 February 2026 Accepted: 26 February 2026 Published: 09 March 2026
MSC : 93D09, 93D20, 93D23

This paper investigates the finite-time stability (FTS) of a class of fractional-order fuzzy inertial neural networks (FOFINNs) with time-varying delays. The existing finite-time inequalities for fractional-order systems pose significant theoretical and practical limitations, as they can yield unbounded control inputs when the system state approaches zero. To address this issue, this work introduces a novel finite-time inequality. By incorporating a positive constant into the inequality structure, the proposed method effectively bounds the control signal, ensuring its practical realizability. Utilizing this inequality within a Lyapunov framework alongside an order reduction method (ORM), a composite feedback controller is designed to achieve FTS. Sufficient stability conditions are derived, and an explicit, computable upper bound for the settling time is established. Numerical simulations validate the theoretical results and demonstrate the method's superiority over existing approaches.
- inertial neural network,
- finite-time stability,
- fractional order,
- fuzzy logics
Citation: Tiecheng Zhang, Wenxiang Fang, Liyan Wang, Yulong Lu. Finite-time stability of fractional-order fuzzy inertial neural networks via a new finite-time inequality[J]. AIMS Mathematics, 2026, 11(3): 5936-5953. doi: 10.3934/math.2026245

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Abstract

This paper investigates the finite-time stability (FTS) of a class of fractional-order fuzzy inertial neural networks (FOFINNs) with time-varying delays. The existing finite-time inequalities for fractional-order systems pose significant theoretical and practical limitations, as they can yield unbounded control inputs when the system state approaches zero. To address this issue, this work introduces a novel finite-time inequality. By incorporating a positive constant into the inequality structure, the proposed method effectively bounds the control signal, ensuring its practical realizability. Utilizing this inequality within a Lyapunov framework alongside an order reduction method (ORM), a composite feedback controller is designed to achieve FTS. Sufficient stability conditions are derived, and an explicit, computable upper bound for the settling time is established. Numerical simulations validate the theoretical results and demonstrate the method's superiority over existing approaches.

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