Advertisement

New Results on Robust Finite-Time Passivity for Fractional-Order Neural Networks with Uncertainties

  • Mai Viet Thuan
  • Dinh Cong Huong
  • Duong Thi Hong
Article
  • 81 Downloads

Abstract

In this paper, the robust finite-time passivity for a class of fractional-order neural networks with uncertainties is considered. Firstly, the definition of finite-time passivity of fractional-order neural networks is introduced. Then, by using finite-time stability theory and linear matrix inequality approach, new sufficient conditions that ensure the finite-time passivity of the fractional-order neural network systems are derived via linear matrix inequalities which can be effectively solved by various computational tools. Finally, three numerical examples with simulation results are given to illustrate the effectiveness of the proposed method.

Keywords

Fractional order neural networks Finite-time stability Finite-time passivity Linear matrix inequalities 

Notes

Acknowledgements

The authors sincerely thank the anonymous reviewers for their constructive comments that helped improve the quality and presentation of this paper. This paper was revised when the authors were working as researchers at Vietnam Institute for Advance Study in Mathematics (VIASM). Authors would like to thank the VIASM for providing a fruitful research environment and extending support and hospitality during their visit.

References

  1. 1.
    Kilbas A, Srivastava H, Trujillo J (2006) Theory and application of fractional diffrential equations. Elsevier, New YorkGoogle Scholar
  2. 2.
    Li Y, Chen YQ, Podlubny I (2010) Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag–Leffer stability. Comput Math Appl 59(5):1810–1821MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Kaczorek T (2011) Selected problems of fractional systems theory. Springer, BerlinCrossRefzbMATHGoogle Scholar
  4. 4.
    Thuan MV, Huong DC (2018) New results on stabilization of fractional-order nonlinear systems via an LMI approach. Asian J Control. 20(4):1541–1550Google Scholar
  5. 5.
    Zhang S, Chen Y, Yu Y (2017) A survey of fractional-order neural networks. In: ASME 2017 international design engineering technical conferences and computers and information in engineering conference. American Society of Mechanical EngineersGoogle Scholar
  6. 6.
    Wang H, Yu Y, Wen G (2014) Stability analysis of fractional-order Hopfield neural networks with time delays. Neural Netw 55:98–109CrossRefzbMATHGoogle Scholar
  7. 7.
    Wang H, Yu Y, Wen G, Zhang S (2015) Stability analysis of fractional-order neural networks with time delay. Neural Process Lett 42(2):479–500CrossRefGoogle Scholar
  8. 8.
    Yang X, Li C, Song Q (2016) Mittag–Leffler stability analysis on variable-time impulsive fractional order neural networks. Neurocomputing 207:276–286CrossRefGoogle Scholar
  9. 9.
    Zhang S, Yu Y, Yu J (2017) LMI conditions for global stability of fractional-order neural networks. IEEE Trans Neural Netw Learn Syst 28(10):2423–2433MathSciNetCrossRefGoogle Scholar
  10. 10.
    Zhang S, Yo Y, Geng L (2017) Stability analysis of fractional-order Hopfield neural networks with time-varying external inputs. Neural Process Lett 45(1):223–241CrossRefGoogle Scholar
  11. 11.
    Wei H, Li R, Chen C, Tu Z (2017) Stability analysis of fractional order complex-valued memristive neural networks with time delays. Neural Process Lett 45(2):379–399CrossRefGoogle Scholar
  12. 12.
    Yang X, Song Q, Liu Y, Zhao Z (2015) Finite-time stability analysis of fractional-order neural networks with delay. Neurocomputing 152:19–26CrossRefGoogle Scholar
  13. 13.
    Dinh X, Cao J, Zhao X, Alsaadi FE (2017) Finite-time stability of fractional-order complex-valued neural networks with time delays. Neural Process Lett 46(2):561–580CrossRefGoogle Scholar
  14. 14.
    Dinh Z, Zeng Z, Wang L (2018) Robust finite-time stabilization of fractional-order neural networks with discontinuous and continuous activation functions under uncertainty. IEEE Trans Neural Netw Learn Syst 29(5):1477–1490Google Scholar
  15. 15.
    Song S, Song X, Balsera IT (2018) Mixed \(H_{\infty }/\)passive projective synchronization for nonidentical uncertain fractional-order neural networks based on adaptive sliding mode control. Neural Process Lett 47(2):443–462Google Scholar
  16. 16.
    Bao H, Park JH, Cao J (2015) Adaptive synchronization of fractional-order memristor-based neural networks with time delay. Nonlinear Dyn 82(3):1343–1354MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Bao H, Park JH, Cao J (2016) Synchronization of fractional-order complex-valued neural networks with time delay. Neural Netw 81:16–28CrossRefGoogle Scholar
  18. 18.
    Hill D, Moylan P (1976) The stability of nonlinear dissipative systems. IEEE Trans Autom Control 21:708–711MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Brogliato B, Maschke B, Lozano R, Egeland O (2007) Dissipative systems analysis and control: theory and applications. Springer, LondonCrossRefzbMATHGoogle Scholar
  20. 20.
    Mathiyalagan K, Park JH, Sakthivel R (2015) New results on passivity-based \(H_{\infty }\) control for networked cascade control systems with application to power plant boiler-turbine system. Nonlinear Anal Hybrid Syst 17:56–69MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Wu A, Zeng Z (2014) Passivity analysis of memristive neural networks with different memductance functions. Commun Nonlinear Sci Numer Simulat 19:274–285MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Zeng HB, Park JH, Shen H (2015) Robust passivity analysis of neural networks with discrete and distributed delays. Neurocomputing 149:1092–1097CrossRefGoogle Scholar
  23. 23.
    Velmurugan G, Rakkiyappan R, Lakshmanan S (2015) Passivity analysis of memristor-based complex-valued neural networks with time-varying delays. Neural Process Lett 42(3):517–540CrossRefGoogle Scholar
  24. 24.
    Thuan MV, Trinh H, Hien LV (2016) New inequality-based approach to passivity analysis of neural networks with interval time-varying delay. Neurocomputing 194:301–307CrossRefGoogle Scholar
  25. 25.
    Nagamani G, Radhika T (2016) Dissipativity and passivity analysis of Markovian jump neural networks with two additive time-varying delays. Neural Process Lett 44(2):571–592CrossRefzbMATHGoogle Scholar
  26. 26.
    Huang Y, Ren S (2017) Passivity and passivity-based synchronization of switched coupled reaction–diffusion neural networks with state and spatial diffusion couplings. Neural Process Lett 47(2):347–363Google Scholar
  27. 27.
    Mathiyalagan K, Anbuvithya R, Sakthivel R, Park JH, Prakash P (2016) Non-fragile \(H_{\infty }\) synchronization of memristor-based neural networks using passivity theory. Neural Netw 74:85–100CrossRefGoogle Scholar
  28. 28.
    He S, Liu F (2014) Optimal finite-time passive controller design for uncertain nonlinear Markovian jumping systems. J Franklin Inst 351(7):3782–3796MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Qi W, Gao X, Wang J (2016) Finite-time passivity and passification for stochastic time-delayed Markovian switching systems with partly known transition rates. Circuits Syst Signal Process 35(11):3913–3934CrossRefzbMATHGoogle Scholar
  30. 30.
    Song J, He S (2015) Finite-time robust passive control for a class of uncertain Lipschitz nonlinear systems with time-delays. Neurocomputing 159:275–281CrossRefGoogle Scholar
  31. 31.
    Mathiyalagan K, Park JH, Sakthivel R (2016) Novel results on robust finite-time passivity for discrete-time delayed neural networks. Neurocomputing 177:585–593CrossRefGoogle Scholar
  32. 32.
    Rajavel S, Samidurai R, Cao J, Alsaedi A, Ahmad B (2017) Finite-time non-fragile passivity control for neural networks with time-varying delay. Appl Math Comput 297:145–158MathSciNetzbMATHGoogle Scholar
  33. 33.
    Li C, Deng W (2007) Remarks on fractional derivatives. Appl Math Comput 187(2):777–784MathSciNetzbMATHGoogle Scholar
  34. 34.
    Amato F, Ariola M, Dorato P (2001) Finite-time control of linear systems subject to parametric uncertainties and disturbances. Automatica 37:1459–1463CrossRefzbMATHGoogle Scholar
  35. 35.
    Ma Y, Wu B, Wang YE (2016) Finite-time stability and finite-time boundedness of fractional order linear systems. Neurocomputing 173:2076–2082CrossRefGoogle Scholar
  36. 36.
    Duarte-Mermoud MA, Aguila-Camacho N, JGallegos JA, Castro-Linares R (2015) Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems. Commun Nonlinear Sci Numer Simulat 22:650–659MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Boyd S, Ghaoui LE, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, PhiladelphiaCrossRefzbMATHGoogle Scholar
  38. 38.
    Wu R, Lu Y, Chen L (2015) Finite-time stability of fractional delayed neural networks. Neurocomputing 149:700–707CrossRefGoogle Scholar
  39. 39.
    Chen L, Liu C, Wu R, He Y, Chai Y (2016) Finite-time stability criteria for a class of fractional-order neural networks with delay. Neural Comput Appl 27(3):549–556CrossRefGoogle Scholar
  40. 40.
    Wang L, Song Q, Liu Y, Zhao Z, Alsaadi FE (2017) Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with both leakage and time-varying delays. Neurocomputing 245:86–101CrossRefGoogle Scholar
  41. 41.
    Zhang H, Ye R, Cao R, Ahmed A, Li X, Wan Y (2018) Lyapunov functional approach to stability analysis of Riemann–Liouville fractional neural networks with time-varying delays. Asian J Control 20(6):1–14MathSciNetGoogle Scholar
  42. 42.
    Kaslik E, Sivasundaram S (2012) Nonlinear dynamics and chaos in fractional-order neural networks. Neural Netw 32:245–256CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and InformaticsThainguyen University of ScienceThai NguyenVietnam
  2. 2.Department for Management of Science and Technology DevelopmentTon Duc Thang UniversityHo Chi Minh CityVietnam
  3. 3.Faculty of Applied SciencesTon Duc Thang UniversityHo Chi Minh CityVietnam

Personalised recommendations