Some novel results for DNNs via relaxed Lyapunov functionals

Guoyi Li; Jun Wang; Kaibo Shi; Yiqian Tang; Guoyi Li; Jun Wang; Kaibo Shi; Yiqian Tang

doi:10.3934/mmc.2024010

Mathematical Modelling and Control

2024, Volume 4, Issue 1: 110-118. doi: 10.3934/mmc.2024010

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Research article

Some novel results for DNNs via relaxed Lyapunov functionals

Guoyi Li ¹,
Jun Wang ^{1
,
,},
Kaibo Shi ^{2
,
,},
Yiqian Tang ²

1.
Electronic Information Engineering Key Laboratory of Electronic Information of State Ethnic Affairs Commission, College of Electrical Engineering, Southwest Minzu University, Chengdu 610041, China
2.
School of Electronic Information and Electrical Engineering, Chengdu University, Chengdu 610106, China

Received: 03 October 2023 Revised: 10 January 2024 Accepted: 04 February 2024 Published: 02 April 2024

The focus of this paper was to explore the stability issues associated with delayed neural networks (DNNs). We introduced a novel approach that departs from the existing methods of using quadratic functions to determine the negative definite of the Lyapunov-Krasovskii functional's (LKFs) derivative $ \dot{V}(t) $. Instead, we proposed a new method that utilizes the conditions of positive definite quadratic function to establish the positive definiteness of LKFs. Based on this approach, we constructed a novel the relaxed LKF that contains delay information. In addition, some combinations of inequalities were extended and used to reduce the conservatism of the results obtained. The criteria for achieving delay-dependent asymptotic stability were subsequently presented in the framework of linear matrix inequalities (LMIs). Finally, a numerical example confirmed the effectiveness of the theoretical result.
Citation: Guoyi Li, Jun Wang, Kaibo Shi, Yiqian Tang. Some novel results for DNNs via relaxed Lyapunov functionals[J]. Mathematical Modelling and Control, 2024, 4(1): 110-118. doi: 10.3934/mmc.2024010

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Abstract

The focus of this paper was to explore the stability issues associated with delayed neural networks (DNNs). We introduced a novel approach that departs from the existing methods of using quadratic functions to determine the negative definite of the Lyapunov-Krasovskii functional's (LKFs) derivative $ \dot{V}(t) $. Instead, we proposed a new method that utilizes the conditions of positive definite quadratic function to establish the positive definiteness of LKFs. Based on this approach, we constructed a novel the relaxed LKF that contains delay information. In addition, some combinations of inequalities were extended and used to reduce the conservatism of the results obtained. The criteria for achieving delay-dependent asymptotic stability were subsequently presented in the framework of linear matrix inequalities (LMIs). Finally, a numerical example confirmed the effectiveness of the theoretical result.

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