Article
Computer Science, Artificial Intelligence
Chenyang Shi, Kachon Hoi, Seakweng Vong
Summary: This paper discusses the exponential stability of neural networks with time-varying delay. A novel integral inequality is derived by extending the generalized free-weighting-matrix integral inequality and using weighted orthogonal functions. The new inequality is then applied to investigate the exponential stability of time delay neural networks via an improved Lyapunov-Krasovskii functional, with numerical examples provided to demonstrate the advantages of the proposed criterion.
Article
Mathematics, Applied
Chen-Rui Wang, Yong He, Wen-Juan Lin
Summary: This paper introduces an improved augmented Lyapunov-Krasovskii functional to address the stability analysis issue of generalized neural networks with fast-varying delay. By utilizing specific methods and strategies based on the augmented LKF, a less conservative delay-dependent stability criterion is proposed. Numerical examples demonstrate the effectiveness of this criterion.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Automation & Control Systems
Xiaonan Liu, Minghui Song, Yonggui Kao
Summary: This paper investigates the synchronization between two hyperbolic coupled networks (HCNs) with time-varying delays using aperiodically intermittent pinning control (AIPC). Sufficient criteria for HCNs with internal delays only and with hybrid delays are obtained based on a Lyapunov function with a piecewise continuous function. It is found that HCNs with hybrid delays have a slower convergence speed compared to those with internal delays only. Additionally, two simulation results are presented to validate the theoretical findings.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
N. Jayanthi, R. Santhakumari, Grienggrai Rajchakit, Nattakan Boonsatit, Anuwat Jirawattanapanit
Summary: This study investigates the asymptotic and cluster synchronization issues of coupled delayed complex-valued neural network models with leakage delay in finite time. Several sufficient conditions for asymptotic synchronization and finite-time synchronization are described utilizing the Lyapunov theory and the Filippov regularization framework.
Article
Automation & Control Systems
Xu Li, Haibo Liu, Kuo Liu, Te Li, Yongqing Wang
Summary: The paper investigates the application of the Lyapunov-Krasovskii functional method in neural networks and proposes a generalized LKF method to derive new exponential stability criteria by weakening the strong condition. The effectiveness of the derived criteria is verified through two numerical examples.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2021)
Article
Computer Science, Artificial Intelligence
Chenyang Shi, Kachon Hoi, Seakweng Vong
Summary: This paper studies the stability of a neural network with time-varying delay. Two general inequalities with two and three terms are derived to estimate the derivative of the Lyapunov-Krasovskii functionals (LKFs). The LKF method is used to develop a stability criterion for time-delay neural networks by using these new inequalities. Numerical results are provided to demonstrate the improvement of the new criterion.
Article
Mathematics
Saravanan Shanmugam, Rajarathinam Vadivel, Nallappan Gunasekaran
Summary: In this paper, a finite-time synchronization method is proposed for quantized Markovian-jump time-varying delayed neural networks (QMJTDNNs) via event-triggered control. The method takes into account the effects of quantization and uses a combination of finite-time synchronization and event-triggered communication to achieve efficient synchronization. The proposed method is analyzed for its finite-time synchronization and convergence properties, and simulation results demonstrate its effectiveness in synchronizing a network of QMJTDNNs. A new method for achieving finite-time synchronization of a system with input constraints is introduced, which involves the use of Lyapunov-Krasovskii functional approach, integral inequality techniques, and linear matrix inequalities. Additionally, the study presents the design of an event-triggered controller gain for a larger sampling interval. The effectiveness of the proposed method is verified through numerical examples.
Article
Mathematics, Interdisciplinary Applications
Huichao Lin, Hongbing Zeng, Wei Wang
Summary: This paper focuses on the delay-dependent stability of linear systems with time-varying delay, presenting a new augmented Lyapunov-Krasovskii functional and less conservative stability criteria. The effectiveness and superiority of the criteria are verified through two well-known numerical examples.
JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
(2021)
Article
Mathematics, Applied
Xu-Kang Chang, Yong He, Zhen-Man Gao
Summary: This article investigates the problem of global exponential stability of neural networks with a time-varying delay. By establishing an improved augmented delay-product-type Lyapunov-Krasovskii functional and utilizing the cross-term relationships and negative-determination lemma, a stability criterion is obtained.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Engineering, Multidisciplinary
K. Udhayakumar, S. Shanmugasundaram, Ardak Kashkynbayev, K. Janani, R. Rakkiyappan
Summary: This paper explores the synchronization of inertial neural networks (INNs) with time-varying delay and coupling delays using control systems with saturated and asymmetrically saturated impulses. Theoretical discussions introduce mixed delays for INNs, and the addressed model is transformed into first-order differential equations using variable transformation and dead-zone function. Adequate conditions for exponential synchronization are derived, and an asymmetric saturated impulsive control approach is proposed for achieving exponential synchronization in the leader-following synchronization pattern of INNs. Simulation results validate the theoretical findings.
APPLIED MATHEMATICAL MODELLING
(2023)
Article
Mathematics, Interdisciplinary Applications
Nian Fuzhong, Li Jia
Summary: The problem of exponential module-phase synchronization of complex-valued neural networks with time-varying delay and stochastic perturbations was investigated. The appropriate controller was designed based on Lyapunov stability theory to control the networks, and the effectiveness and reliability of the method were verified through numerical simulations.
JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
(2021)
Article
Computer Science, Artificial Intelligence
Yong Zhao, Shanshan Ren, Juergen Kurths
Summary: This paper discusses the synchronization of coupled memristive competitive BAM neural networks with different time scales, and proposes novel sufficient conditions to achieve synchronization. The research results demonstrate the feasibility and ease of implementation of the proposed synchronization method.
Article
Mathematics, Applied
Saravanan Shanmugam, R. Vadivel, Mohamed Rhaima, Hamza Ghoudi
Summary: This research investigates the issue of extended dissipative analysis for neural networks with additive time-varying delays. By constructing the augmented Lyapunov-Krasovskii functional and utilizing improved integral inequalities, such as auxiliary function-based integral inequalities, less conservative sufficient conditions are obtained to ensure the asymptotic stability and extended dissipativity of the neural networks. The study aims to solve the H_∞, L_2 - L_∞, passivity, and (Q, S, R)-γ-dissipativity performance problems in a unified framework based on the concept of extended dissipativity. The solvability condition of the designed neural networks with additive time-varying delays is presented in the form of linear matrix inequalities. Finally, the practicality and effectiveness of this approach are demonstrated through four numerical examples.
Article
Computer Science, Information Systems
Sapna Baluni, Vijay K. Yadav, Subir Das
Summary: This article investigates the quasi-projective synchronization of time-varying delayed complex-valued Cohen Grossberg Neural Networks (CGNNs). The study aims to find a criterion for quasi-projective synchronization of two non-identical CGNNs by constructing a suitable controller and utilizing the direct method. The significant contribution is estimating the bound of the synchronization error and establishing sufficient criteria for synchronization. The proposed method's effectiveness is justified through numerical simulation in a specific example.
INFORMATION SCIENCES
(2022)
Article
Computer Science, Artificial Intelligence
Yin Sheng, Tingwen Huang, Zhigang Zeng, Xiangshui Miao
Summary: This article investigates the Lagrange exponential stability and the Lyapunov exponential stability of memristive neural networks with discrete and distributed time-varying delays. The study uses inequality techniques, theories of the M-matrix, and the comparison strategy to consider the stability of the networks, providing less conservative methods for analyzing Lyapunov stability.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2021)
