Accuracy-preassigned fixed-time synchronization of inertial neural networks with time-varying leakage delays and proportional delays

Er-Yong Cong; Xian Zhang; Li Zhu; Er-Yong Cong; Xian Zhang; Li Zhu

doi:10.3934/era.2025262

Electronic Research Archive

2025, Volume 33, Issue 10: 5897-5915. doi: 10.3934/era.2025262

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Accuracy-preassigned fixed-time synchronization of inertial neural networks with time-varying leakage delays and proportional delays

Er-Yong Cong ^{1,2
,
,},
Xian Zhang ^{3,4
,
,},
Li Zhu ¹

1.
Department of Mathematics, Harbin University, Harbin 150086, China
2.
Heilongjiang Provincial Key Laboratory of the Intelligent Perception and Intelligent Software, Harbin University, Harbin 150080, China
3.
School of Mathematical Science, Heilongjiang University, Harbin 150080, China
4.
Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems, Heilongjiang University, Harbin 150080, China

Received: 26 July 2025 Revised: 19 September 2025 Accepted: 26 September 2025 Published: 09 October 2025

This work established synchronization criteria for master-slave inertial neural networks with leakage time-varying delays and proportional delays, The solution employed a direct analysis method based on parameterized system solutions. The derived synchronization conditions consisted of only a few simple inequalities, which were easy to solve.Based on the adopted approach, a novel class of synchronization controllers was designed for proportional delays without constructing any complex functionals. Using the proposed method, leakage delays could be transformed into their maximum absolute values, enabling the derivation of delay-dependent conditions without any intricate treatment of leakage delays. Furthermore, it was noteworthy that this paper presented the first investigation into this problem using the proposed method, and the technique employed was novel. Finally, numerical simulations were provided to verify the effectiveness of the proposed method.
Citation: Er-Yong Cong, Xian Zhang, Li Zhu. Accuracy-preassigned fixed-time synchronization of inertial neural networks with time-varying leakage delays and proportional delays[J]. Electronic Research Archive, 2025, 33(10): 5897-5915. doi: 10.3934/era.2025262

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Abstract

This work established synchronization criteria for master-slave inertial neural networks with leakage time-varying delays and proportional delays, The solution employed a direct analysis method based on parameterized system solutions. The derived synchronization conditions consisted of only a few simple inequalities, which were easy to solve.Based on the adopted approach, a novel class of synchronization controllers was designed for proportional delays without constructing any complex functionals. Using the proposed method, leakage delays could be transformed into their maximum absolute values, enabling the derivation of delay-dependent conditions without any intricate treatment of leakage delays. Furthermore, it was noteworthy that this paper presented the first investigation into this problem using the proposed method, and the technique employed was novel. Finally, numerical simulations were provided to verify the effectiveness of the proposed method.

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