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Finite-time stability on a class of SICNNs with neutral proportional delays

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Abstract

In this paper, the finite-time stability for a class of shunting inhibitory cellular neural networks with neutral proportional delays is discussed. By employing differential inequality techniques, several sufficient conditions are obtained to ensure the finite-time stability for the considered neural networks. Meanwhile, the generalized exponential synchronization is also established. An example along with its numerical simulation is presented to demonstrate the validity of the proposed results.

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References

  1. Hien LV (2014) An explicit criterion for finite-time stability of linear nonautonomous systems with delays. Appl Math Lett 30:12–18

    Article  MathSciNet  MATH  Google Scholar 

  2. Erneux T (2009) Applied delay differential equations. Springer, New York

    MATH  Google Scholar 

  3. Phat VN, Hien LV (2009) An application of Razumikhin theorem to exponential stability for linear non-autonomous systems with time-varying delay. Appl Math Lett 22:1412–1417

    Article  MathSciNet  MATH  Google Scholar 

  4. Ngoc PHA (2012) On exponential stability of nonlinear differential systems with time-varying delay. Appl Math Lett 25:1208–1213

    Article  MathSciNet  MATH  Google Scholar 

  5. Song B, Park JH, Wu ZG, Zhang Y (2013) New results on delay-dependent stability analysis for neutral stochastic delay systems. J Franklin Inst 350:840–852

    Article  MathSciNet  MATH  Google Scholar 

  6. Seuret A, Gouaisbaut F (2013) Wirtinger-based integral inequality: application to time-delay systems. Automatica 49:2860–2866

    Article  MathSciNet  MATH  Google Scholar 

  7. Bouzerdoum A, Pinter RB (1993) Shunting inhibitory cellular neural networks: derivation and stability analysis. IEEE Trans Circuits Syst 1 Fundam Theory Appl 40:215–221

    Article  MathSciNet  MATH  Google Scholar 

  8. Bouzerdoum A, Pinter RB (1991) Analysis and analog implementation of directionally sensitive shunting inhibitory cellular neural networks. Visual Inf Process Neurons Chips SPIE 1473:29–38

    Article  Google Scholar 

  9. Bouzerdoum A, Pinter RB (1992) Nonlinear lateral inhibition applied to motion detection in the fly visual system. In: Pinter RB, Nabet B (eds) Nonlinear Vision. CRC Press, Boca Raton, pp 423–450

    Google Scholar 

  10. Chen Z (2013) A shunting inhibitory cellular neural network with leakage delays and continuously distributed delays of neutral type. Neural Comput Appl 23:2429–2434

    Article  Google Scholar 

  11. Liu B (2015) Pseudo almost periodic solutions for neutral type CNNs with continuously distributed leakage delays. Neurocomputing 148:445–454

    Article  Google Scholar 

  12. Liu X (2015) Exponential convergence of SICNNs with delays and oscillating coefficients in leakage terms. Neurocomputing 168:500–504

    Article  Google Scholar 

  13. Zhao C, Wang Z (2015) Exponential convergence of a SICNN with leakage delays and continuously distributed delays of neutral type. Neural Process Lett. 41:239–247

    Article  Google Scholar 

  14. Ockendon JR, Tayler AB (1971) The dynamics of a current collection system for an electric locomotive. Proc R Soc A 322:447–468

    Article  Google Scholar 

  15. Fox L, Mayers DF, Ockendon JR, Tayler AB (1971) On a functional-differential equation. J Inst Math Appl 8(3):271–307

    Article  MathSciNet  MATH  Google Scholar 

  16. Derfel GA (1982) On the behaviour of the solutions of functional and functional-differential equations with several deviating arguments. Ukr Math J 34:286–291

    Article  MATH  Google Scholar 

  17. Derfel GA (1990) Kato problem for functional-differential equations and difference Schrödinger operators. Oper Theory 46:319–321

    MATH  Google Scholar 

  18. Ockendon JR, Tayler AB (1971) The dynamics of a current collection system for an electric locomotive. Proc R Soc A 322:447–468

    Article  Google Scholar 

  19. Fox L, Mayers DF, Ockendon JR, Tayler AB (1971) On a functional-differential equation. J Inst Math Appl 8(3):271–307

    Article  MathSciNet  MATH  Google Scholar 

  20. Derfel GA (1982) On the behaviour of the solutions of functional and functional-differential equations with several deviating arguments. Ukr Math J 34:286–291

    Article  MATH  Google Scholar 

  21. Song X, Zhao P, Xing Z, Peng J (2016) Global asymptotic stability of CNNs with impulses and multi-proportional delays. Appl Sci Math Methods 39:722–733

    Article  MathSciNet  MATH  Google Scholar 

  22. Derfel GA (1990) Kato problem for functional-differential equations and difference Schrödinger operators. Oper Theory 46:319–321

    MATH  Google Scholar 

  23. Karafyllis I (2006) Finite-time global stabilization by means of time-varying distributed delay feedback. SIAM J Control Optim 45:320–342

    Article  MathSciNet  MATH  Google Scholar 

  24. Moulay E, Dambrine M, Yeganefar N, Perruquetti W (2008) Finite-time stability and stabilization of time-delay systems. Syst Control Lett 57:561–566

    Article  MathSciNet  MATH  Google Scholar 

  25. Yang R, Wang Y (2012) Finite-time stability and stabilization of a class of nonlinear time-delay systems. SIAM J Control Optim 50(5):3113–3131

    Article  MathSciNet  MATH  Google Scholar 

  26. Yang R, Wang Y (2013) Finite-time stability analysis and H control for a class of nonlinear time-delay Hamiltonian systems. Automatica 49:390–401

    Article  MathSciNet  MATH  Google Scholar 

  27. Efimov D, Polyakov A, Fridman E, Perruquetti W, Richard JP (2014) Comments on finite-time stability of time-delay systems. Automatica 50:1944–1947

    Article  MathSciNet  MATH  Google Scholar 

  28. Amato F, Ambrosino R, Ariola M, Cosentino C, De Tomasi G (2014) Finite-time stability and control. Springer, London

    Book  MATH  Google Scholar 

  29. Garcia G, Tarbouriech S, Bernussou J (2009) Finite-time stabilization of linear time-varying continuous systems. IEEE Trans Autom Control 54:364–369

    Article  MathSciNet  MATH  Google Scholar 

  30. Amato F, Ariola M, Cosentino C (2010) Finite-time control of discrete-time linear systems: analysis and design conditions. Automatica 46:919–924

    Article  MathSciNet  MATH  Google Scholar 

  31. Yu Y (2016) Finite-time stability on a class of non-autonomous SICNNs with multi-proportional delays. Asian J Control. doi:10.1002/asjc.1323

    Google Scholar 

  32. Liu B (2016) Finite-time stability of  CNNs with neutral proportional delays and time-varying leakage delays. Appl Sci Math Methods. doi:10.1002/mma.3976

    MATH  Google Scholar 

  33. Hien L, Son DT (2015) Finite-time stability of a class of non-autonomous neural networks with heterogeneous proportional delays. Appl Math Comput 251:14–23

    MathSciNet  MATH  Google Scholar 

  34. Chen T, Wang L (2007) Power-rate global stability of dynamical systems with unbounded time-varying delays. IEEE Trans Circuits Syst II Express Briefs 54(8):705–709

    Article  Google Scholar 

  35. Chen T, Wang L (2007) Global \(\mu\)-stability of delayed neural networks with unbounded time-varying delays. IEEE Trans Neural Netw 18(8):1836–1840

    Article  Google Scholar 

  36. Wang L, Chen T (2014) Multiple \(\mu\)-stability of neural networks with unbounded time-varying delays. Neural Netw 53:109–118

    Article  MATH  Google Scholar 

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Acknowledgments

The author thanks for the anonymous referees valuable opinions. The suggestions improve this paper and motivate some further works.

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Correspondence to Yuehua Yu.

Additional information

This work was supported by the Natural Scientific Research Fund of Hunan Provincial of China (Grant Nos. 2016JJ6103, 2016JJ6104), and the Construction Program of the Key Discipline in Hunan University of Arts and Science−Applied Mathematics.

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Yu, Y. Finite-time stability on a class of SICNNs with neutral proportional delays. Neural Comput & Applic 28 (Suppl 1), 97–105 (2017). https://doi.org/10.1007/s00521-016-2295-7

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  • DOI: https://doi.org/10.1007/s00521-016-2295-7

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