PERIODICITY AND FIXED-TIME STABILIZATION OF DISCONTINUOUS NEURAL NETWORKS WITH MIXED DELAYS: UNBOUNDED DELAY-DEPENDENT CRITERIA

doi:10.1007/s10473-025-0323-3

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (3): 1188-1204.doi: 10.1007/s10473-025-0323-3

PERIODICITY AND FIXED-TIME STABILIZATION OF DISCONTINUOUS NEURAL NETWORKS WITH MIXED DELAYS: UNBOUNDED DELAY-DEPENDENT CRITERIA

Ziwei WANG¹, Lin SUN¹, Fanchao KONG^2,†, Rathinasamy SAKTHIVEL³

1. School of Finance, Hunan University of Finance and Economics, Changsha 410205, China;
2. School of Mathematics and Statistics, Anhui Normal University, Wuhu 241000, China;
3. Department of Applied Mathematics, Bharathiar University, Coimbatore 641046, India

收稿日期:2023-08-11 修回日期:2024-05-15 出版日期:2025-05-25 发布日期:2025-09-30

PERIODICITY AND FIXED-TIME STABILIZATION OF DISCONTINUOUS NEURAL NETWORKS WITH MIXED DELAYS: UNBOUNDED DELAY-DEPENDENT CRITERIA

Ziwei WANG¹, Lin SUN¹, Fanchao KONG^2,†, Rathinasamy SAKTHIVEL³

1. School of Finance, Hunan University of Finance and Economics, Changsha 410205, China;
2. School of Mathematics and Statistics, Anhui Normal University, Wuhu 241000, China;
3. Department of Applied Mathematics, Bharathiar University, Coimbatore 641046, India

Received:2023-08-11 Revised:2024-05-15 Online:2025-05-25 Published:2025-09-30
Contact: ^†Fanchao KONG, E-mail: fanchaokong88@ahnu.edu.cn
About author:Ziwei WANG, E-mail: hnu517@163.com; Lin SUN, E-mail: 43356972@qq.com; Rathinasamy SAKTHIVEL, E-mail: krsakthivel0209@gmail.com
Supported by:
Social Science Fund of Hunan province (Grant No.22JD074) and the Research Foundation of Education Bureau of Hunan province (Grant No.22B0912).

摘要/Abstract

摘要： In this paper, a class of discontinuous neutral-type neural networks (NTNNs) with proportional delays is considered. The targets of the paper are to study the problem of periodic solutions and fixed-time (FXT) stabilization of the addressed neural networks. In order to complete the targets, based on set-valued map, differential inclusions theory, coincidence theorem and Hölder inequality technique, some new proportional delay-dependent criteria shown by the inequalities are derived. Based on the fact of the existence of solution, further by applying the FXT stability lemmas and equivalent transformation, the zero solution of closed-loop system achieves FXT stabilization and the corresponding settling-times are estimated. Some previous related works on NTNNs are extended. Finally, one typical example is provided to show the effectiveness of the established results.

关键词: Fixed-time stabilization, Periodic solutions, Discontinuous neural systems, Differential inclusions theory, Proportional delays

Abstract: In this paper, a class of discontinuous neutral-type neural networks (NTNNs) with proportional delays is considered. The targets of the paper are to study the problem of periodic solutions and fixed-time (FXT) stabilization of the addressed neural networks. In order to complete the targets, based on set-valued map, differential inclusions theory, coincidence theorem and Hölder inequality technique, some new proportional delay-dependent criteria shown by the inequalities are derived. Based on the fact of the existence of solution, further by applying the FXT stability lemmas and equivalent transformation, the zero solution of closed-loop system achieves FXT stabilization and the corresponding settling-times are estimated. Some previous related works on NTNNs are extended. Finally, one typical example is provided to show the effectiveness of the established results.

Key words: Fixed-time stabilization, Periodic solutions, Discontinuous neural systems, Differential inclusions theory, Proportional delays

中图分类号:

34A36

Ziwei WANG, Lin SUN, Fanchao KONG, Rathinasamy SAKTHIVEL. PERIODICITY AND FIXED-TIME STABILIZATION OF DISCONTINUOUS NEURAL NETWORKS WITH MIXED DELAYS: UNBOUNDED DELAY-DEPENDENT CRITERIA[J]. 数学物理学报(英文版), 2025, 45(3): 1188-1204.

Ziwei WANG, Lin SUN, Fanchao KONG, Rathinasamy SAKTHIVEL. PERIODICITY AND FIXED-TIME STABILIZATION OF DISCONTINUOUS NEURAL NETWORKS WITH MIXED DELAYS: UNBOUNDED DELAY-DEPENDENT CRITERIA[J]. Acta mathematica scientia,Series B, 2025, 45(3): 1188-1204.

参考文献

[1] Ali M S, Saravanan S. Robust finite-time $H^\infty$ control for a class of uncertain switched neural networks of neutral-type with distributed time varying delays. Neurocomputing, 2016, 177: 454-468
[2] Aouiti C, Assali E, Ben Gharbia I. Global exponential convergence of neutral type competitive neural networks with D-operator and mixed delay. Journal of Systems Science & Complexity, 2020, 33: 1785-1803
[3] Arik S. A modified Lyapunov functional with application to stability of neutral-type neural networks with time delays. Journal of the Franklin Institute, 2019, 356: 276-291
[4] Arik S. New criteria for stability of neutral-type neural networks with multiple time delays. IEEE Transactions on Neural Networks and Learning Systems, 2020, 31: 1504-1513
[5] Aubin J P, Cellina A. Differential Inclusions.Berlin, Germany: Sprigner-Verlag, 1984
[6] Cai Z W, Huang L H. Generalized Lyapunov approach for functional differential inclusions. Automatica, 2020, 113: 108740
[7] Cai Z W, Huang J C, Huang L H. Generalized Lyapunov Razumikhin method for retarded differential inclusions: Applications to discontinuous neural networks. Discrete & Continuous Dynamical Systems Series B, 2017, 22: 3591-3614
[8] Cortés J. Discontinuous dynamical systems. IEEE Control Systems Magazine, 2008, 28: 36-73
[9] Dovrolis C, Stiliadis D, Ramanathan P. Proportional differentiated services: Delay differentiation and packet scheduling. IEEE/ACM Transactions On Networking, 2002, 10: 12-26
[10] Faydasicok O. Further stability analysis of neutral-type Cohen-Grossberg neural networks with multiple delays. Discrete and Continuous Dynamical Systems-Series S, 2021, 14: 1245-1258
[11] Faydasicok O. An improved Lyapunov functional with application to stability of Cohen-Grossberg neural networks of neutral-type with multiple delays. Neural Networks, 2020, 132: 532-539
[12] Filippov A F.Differential Equations with Discontinuous Right-hand Sides: Control systems. Dordrecht: Kluwer Academic, 1988
[13] Guo Z Y, Huang L H. Generalized Lyapunov method for discontinuous systems. Nonlinear Analysis: Theory, Methods & Applications, 2009, 71: 3083-3092
[14] Hale J.Theory of Functional Differential Equations. New York: Springer, 1977
[15] Hu C, Yu J, Chen Z, et al. Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks. Neural Networks, 2017, 89: 74-83
[16] Huang L H, Guo Z Y, Wang J F.Theory and Applications of Differential Equations with Discontinuous Right-hand Sides
(in Chinese). Beijing: Science Press, 2011
[17] Huang C X, Su R, Cao J D, Xiao L. Asymptotically stable high-order neutral cellular neural networks with proportional delays and D operators. Mathematics and Computers in Simulation, 2020, 171: 127-135
[18] Khalil H K, Grizzle J W. Nonlinear Systems. New Jersey: Prentice Hall, 2002
[19] Kong F C, Zhu Q X, Wang K, Nieto J J. Stability analysis of almost periodic solutions of discontinuous BAM neural networks with hybrid time-varying delays and $D$ operator. Journal of the Franklin Institute, 2019, 356: 11605-11637
[20] Kong F C, Zhu Q X, Huang T W. New fixed-time stability lemmas and applications to the discontinuous fuzzy inertial neural networks. IEEE Transactions on Fuzzy Systems, 2021, 29: 3711-3722
[21] Kong F C, Ren Y, Sakthivel R. New criteria on periodicity and stabilization of discontinuous uncertain inertial Cohen-Grossberg neural networks with proportional delays. Chaos, Solitons & Fractals, 2021, 150: 111148
[22] Kong F C, Zhu Q X. New fixed-time synchronization control of discontinuous inertial neural networks via indefinite Lyapunov-Krasovskii functional method. International Journal of Robust and Nonlinear Control, 2021, 31: 471-495
[23] Kong F C, Zhu Q X. Fixed-time stabilization of discontinuous neutral neural networks with proportional delays via new fixed-time stability lemmas. IEEE Transactions on Neural Networks and Learning Systems, 2023, 34: 775-785
[24] Li W, Ji J, Huang L. Dynamics of a controlled discontinuous computer worm system. Proceedings of the American Mathematical Society, 2020, 148: 4389-4403
[25] Li Y, Lin Z H. Periodic solutions of differential inclusions. Nonlinear Analysis: Theory, Methods and Applications, 1995, 24: 631-641
[26] Wang Z Y, Cao J D, Cai Z W, Abdel-Aty M. A novel Lyapunov theorem on finite/fixed-time stability of discontinuous impulsive systems. Chaos, 2020, 30: 013139
[27] Wang Z Y, Cao J D, Cai Z W, Xue C F.A novel fixed-time stability of nonlinear impulsive systems: A two-stage comparison principle method. International Journal of Systems Science, 2021, 52: 2114-2128
[28] Wang W P, Li L X, Peng H P, et al.Anti-synchronization of coupled memristive neutral-type neural networks with mixed time-varying delays via randomly occurring control. Nonlinear Dynamics, 2016, 83: 2143-2155
[29] Wang L M, Zeng Z G, Hu J, Wang X. Controller design for global fixed-time synchronization of delayed neural networks with discontinuous activations. Neural Networks, 2017, 87: 122-131
[30] Wang K, Zhu Y L. Stability of almost periodic solution for a generalized neutral-type neural networks with delays. Neurocomputing, 2010, 73: 3300-3307
[31] Ozcan N. Stability analysis of Cohen-Grossberg neural networks of neutral-type: Multiple delays case. Neural Networks, 2019, 113: 20-27
[32] Polyakov A.Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Transactions on Automatic Control, 2012, 57: 2106-2110
[33] Samli R, Senan S, Yucel E, Orman Z. Some generalized global stability criteria for delayed Cohen-Grossberg neural networks of neutral-type. Neural Networks, 2019, 116: 198-207
[34] Song Q K, Long L Y, Zhao Z J, et al. Stability criteria of quaternion-valued neutral-type delayed neural networks. Neurocomputing, 2020, 412: 287-294
[35] Xiao J, Zeng Z G, Wen S P, et al. A unified framework design for finite-time and fixed-time synchronization of discontinuous neural networks. IEEE Transactions on Cybernetics, 2021, 51: 3004-3016
[36] Xiao J, Zeng Z G, Wen S P, et al. Finite-/fixed-time synchronization of delayed coupled discontinuous neural networks with unified control schemes. IEEE Transactions on Neural Networks and Learning Systems, 2021, 32: 2535-2546
[37] Xu C J, Li P L. On anti-periodic solutions for neutral shunting inhibitory cellular neural networks with time-varying delays and $D$ operator. Neurocomputing, 2018, 275: 377-382
[38] Yang X, Tian Y, Li X D. Finite-time boundedness and stabilization of uncertain switched delayed neural networks of neutral type. Neurocomputing, 2018, 314: 468-478
[39] Zheng M W, Wang Z M, Li L X, et al. Finite-time generalized projective lag synchronization criteria for neutral-type neural networks with delay. Chaos, Solitons & Fractals, 2018, 107: 195-203
[40] Zou Y, Yang X S, Cheng Z S. Finite-time quantized synchronization of coupled discontinuous competitive neural networks with proportional delay and impulsive effects. Journal of the Franklin Institute, 2020, 357: 11136-11152

PERIODICITY AND FIXED-TIME STABILIZATION OF DISCONTINUOUS NEURAL NETWORKS WITH MIXED DELAYS: UNBOUNDED DELAY-DEPENDENT CRITERIA

PERIODICITY AND FIXED-TIME STABILIZATION OF DISCONTINUOUS NEURAL NETWORKS WITH MIXED DELAYS: UNBOUNDED DELAY-DEPENDENT CRITERIA

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