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Estimation of the Domain of Attraction of Discrete-Time Impulsive Cohen-Grossberg Neural Networks Model With Impulse Input Saturation

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Abstract

This paper aims at estimating the domain of attraction of discrete-time impulsive neural networks with impulse input saturation by using Lyapunov function. When an equilibrium point is locally asymptotically stable, we estimate the size of its domain of attraction and then analyze the effects of impulse input saturation. Two numerical examples are presented to unfold the effectiveness of the theoretical results.

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References

  1. Cohen MA, Grossberg S (1983) Absolute stability and global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans Syst Man Cybernet 13(5):815–826

    Article  MathSciNet  Google Scholar 

  2. Grossberg S (1988) Nonlinear neural networks: principles, mechanisms, and architectures. Neur Netw 1(1):17–61

    Article  Google Scholar 

  3. Song Q, Cao J (2008) Dynamical behaviors of discrete-time fuzzy cellular neural networks with variable delays and impulses. J Franklin Inst 345(1):39–59

    Article  MathSciNet  Google Scholar 

  4. Yang X, Cui X, Long Y (2009) Existence and global exponential stability of periodic solution of a cellular neural networks difference equation with delays and impulses. Neur Netw 22(7):970–976

    Article  Google Scholar 

  5. Liu B, Hill DJ, Sun Z (2018) Input-to-state exponents and related ISS for delayed discrete-time systems with application to impulsive effects. Int J Robust Nonlinear Contr 28(2):640–660

    Article  MathSciNet  Google Scholar 

  6. Li C, Wu S, Feng GG, Liao X (2011) Stabilizing effects of impulses in discrete-time delayed neural networks. IEEE Trans Neur Netw 22(2):323–329

    Article  Google Scholar 

  7. Kaslik E, Sivasundaram S (2011) Impulsive hybrid discrete-time Hopfield neural networks with delays and multistability analysis. Neur Netw 24(4):370–377

    Article  Google Scholar 

  8. Wenlin Jiang (2019) Exponential Lagrange stability for impulses in discrete-time delayed recurrent neural networks. Int J Syst Sci 50(1):50–59

    Article  MathSciNet  Google Scholar 

  9. Sowmiya C, Raja R, Zhu Q, Rajchakit G (2009) Further mean-square asymptotic stability of impulsive discrete-time stochastic BAM neural networks with Markovian jumping and multiple time-varying delays. J Franklin Inst 356(1):561–591

    Article  MathSciNet  Google Scholar 

  10. Hui Li, Yonggui Kao (2019) Synchronous stability of the fractional-order discrete-time dynamical network system model with impulsive couplings. Neurocomputing 363:205–211

    Article  Google Scholar 

  11. Wenjun Xiong (2018) Stability of singular discrete-time neural networks with state-dependent coefficients and run-to-run control strategies. IEEE Trans neur netw learn syst 29(12):6415–6420

    Article  MathSciNet  Google Scholar 

  12. Jinling Wang (2018) A new approach based on discrete-time high-order neural networks with delays and impulses. J Franklin Inst 355(11):4708–4726

    Article  MathSciNet  Google Scholar 

  13. Wang X, Park JuH, Zhao G, Zhong S (2019) An improved fuzzy sampled-data control to stabilization of T-S fuzzy systems with state delays. IEEE Trans Cybern 50(7):3125–3135

    Article  Google Scholar 

  14. Li H, Li C, Huang T, Zhang W (2018) Fixed-time stabilization of impulsive Cohen-Grossberg BAM neural networks. Neur Netw 98:203–211

    Article  Google Scholar 

  15. Li L, Li C, Li H (2018) Fully state constraint impulsive control for non-autonomous delayed nonlinear dynamic systems. Hybrid Systems. Elsevier, Nertherland, Nonlinear Analysis, pp 383–394

    MATH  Google Scholar 

  16. Li L, Li C, Li H (2018) An analysis and design for time-varying structures dynamical networks via state constraint impulsive control. Int J Contr

  17. Li Z, Fang J, Huang T, Miao Q, Wang H (2018) Impulsive synchronization of discrete-time networked oscillators with partial input saturation. Inf Sci 422:531–541

    Article  Google Scholar 

  18. Fangru Meng (2019) Periodicity of Cohen-Grossberg-type fuzzy neural networks with impulses and time-varying delays. Neurocomputing 325:254–259

    Article  Google Scholar 

  19. Chen Y (2006) Global asymptotic stability of delayed Cohen-Grossberg neural networks. IEEE Trans Circuits Syst I, Reg Papers 53(2):351–357

    Article  MathSciNet  Google Scholar 

  20. Zhang H, Wang Z, Liu D (2008) Robust stability analysis for interval Cohen-Grossberg neural networks with unknown time-varying delays. IEEE Trans Neural Netw 19(11):1942–1955

    Article  Google Scholar 

  21. Wardi Y, Seatzu C, Chen X, Yalamanchili S (2016) Performance regulation of event-driven dynamical systems using innitesimal perturbation analysis. Nonlinear Anal Hybrid Syst 22:116–136

    Article  MathSciNet  Google Scholar 

  22. Lei Fu, Ma Y (2016) Passive control for singular time-delay system with actuator saturation. Appl Math Comput 289:181–193

    MathSciNet  MATH  Google Scholar 

  23. Wenhai Qi, Gao X (2016) H-infinity Observer design for stochastic time-delayed systems with Markovian switching under partly known transition rates and actuator saturation. Appl Math Comput 289:80–97

    MathSciNet  MATH  Google Scholar 

  24. Shen Z, Li C, Li H, Cao Z (2019) Estimation of the domain of attraction for discrete-time linear impulsive control systems with input saturation. Appl Math Comput 362

    Article  MathSciNet  Google Scholar 

  25. Lin X, Li X, Zou Y, Li S (2014) Finite-time stabilization of switched linear systems with nonlinear saturating actuators. J Franklin Inst 351(3):1464–1482

    Article  MathSciNet  Google Scholar 

  26. Huang H, Li D, Lin Z, Xi Y (2011) An improved robust model predictive control design in the presence of actuator saturation. Automatica 47(4):861–864

    Article  MathSciNet  Google Scholar 

  27. Rakkiyappan R, Latha V, Zhu Q, Yao Z (2017) Exponential synchronization of markovian jumping chaotic neural networks with sampled-data and saturating actuators. Nonlinear Analy: Hybrid Syst 24:28–44

    MathSciNet  MATH  Google Scholar 

  28. St Balint, Balint AM, Negru V (1986) The optimal Lyapunov function in diagonalizable case. An Univ Timisoara 24(1–2):1–7

    MATH  Google Scholar 

  29. St Balint (1985) Considerations concerning the maneuvering of some physical systems. An Univ Timisoara 23:8–16

    Google Scholar 

  30. Kaslik E, Balint AM, St Balint (2005) Methods for determination and approximation of the domain of attraction. Nonlinear Anal Theor 60(4):703–717

    Article  MathSciNet  Google Scholar 

  31. Liz E, Ferreiro JB (2002) A note on the global stability of generalized difference equations. Appl Math Let 15:655–659

    Article  MathSciNet  Google Scholar 

  32. Jin D, Peng J (2009) A new approach for estimating the attraction domain for Hopfield-type neural networks. Neural Comput 21(1):101–120

    Article  MathSciNet  Google Scholar 

  33. Hu T, Lin Z (2001) Control systems with actuator saturation: analysis and design. Springer Science & Business Media, Berlin

    Book  Google Scholar 

Download references

Acknowledgements

This publication was made possible by the National Natural Science Foundation (61873213, 61633011 and 61906023), and this work was also supported by by the Chongqing Research Program of Basic Research and Frontier Technology of cstc2015jcyjBX0052 and cstc2019jcyj-msxmX0710.

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Authors and Affiliations

  1. National & Local Joint Engineering Laboratory of Intelligent Transmission and Control Technology (Chongqing), College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, China

    Zixiang Shen, Chuandong Li & Yi Li

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  1. Zixiang Shen
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  2. Chuandong Li
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  3. Yi Li
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Correspondence to Chuandong Li.

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Shen, Z., Li, C. & Li, Y. Estimation of the Domain of Attraction of Discrete-Time Impulsive Cohen-Grossberg Neural Networks Model With Impulse Input Saturation. Neural Process Lett 53, 2029–2046 (2021). https://doi.org/10.1007/s11063-021-10498-7

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  • DOI: https://doi.org/10.1007/s11063-021-10498-7

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