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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Synchronization of T-S Fuzzy Sampled-data Controller for H-R Neuron Model With Delay using a New Looped-Functional

Discontinuity, Nonlinearity, and Complexity 10(2) (2021) 259--273 | DOI:10.5890/DNC.2021.06.007

P. Nirvin$^1$ , R. Rakkiyappan$^1$

Department of Mathematics, Bharathiar University, Coimbatore - 641 046, Tamilnadu, India

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Abstract

This paper investigates the synchronization of Takagi-Sugeno (T-S) fuzzy sampled-data-controller for Hindmarsh-Rose (H-R) neuron model with constant {communication time delay} in the from the master-slave framework. The utilization of the state information of $e(t_k),~e(t),~e(t_{k+1}),~e(t_k-\lambda),~e(t-\lambda),~e(t_{k+1}-\lambda)$, is done adequately {be} the information of a novel looped-functional in the construction of a Lyapunov functional (LF). To establish that the slave system is synchronized with the master system, some satisfactory conditions with less conservativeness are derived by using the above mentioned functional and utilizing wirtingers inequality, jensen's inequalities, free matrix-based integral inequality method. The linear matrix inequality (LMI) techniques the fuzzy sampled-data control can be designed. Finally, a numerical example is given to illustrate the effectiveness of our theoretical results.

References

  1. [1]  Gopalsamy, K. and He, X.Z. (1994), {Delay-independent stability in bidirectional associative memory networks,} IEEE Trans. Neural Netw., 5(6), 998-1002.
  2. [2]  Ott, E., Grebogi, C., and York, J.A. (1990), {Controlling chaos,} Phys. Rev. Lett., 1196-1199.
  3. [3]  Jackson, E.A., Hubler, A. (1990), {Periodic entrainment of chaotic logistic map dynamics.} Phys., 404-409. %2
  4. [4]  Livingstone, D.J. (2008), {Artificial Neural Networks: Methods and Applications (Methods in Molecular Biology),} Sandown, U.K.: Humana \underline{Press}.
  5. [5]  Han, Q.L. (2009), {A discrete delay decomposition approach to stability of linear retarded and neutral systems,} Automatica, 517-524.
  6. [6]  Wu, M., He, Y., She, J.H., and Liu, G.P. (2004), {Delay-dependent criteria for robust stability of time-varying delay systems,} Automatica, 1435-1439. %3
  7. [7]  Cavaterra, C. and Grasselli, M. (2009), {Robust exponential attractors for singularly perturbed Hodgkin-Huxley equations,} J. Differ. Equ., 246(12), 4670-4701. %4
  8. [8]  Shilnikov, A. and Kolomiets, M. (2008), {Methods of the qualitative theory for the Hindmarsh-Rose model: A case study-A tutorial,} Int. J. Bifurcation Chaos, 18(8), 2141-2168.
  9. [9]  Beyhan, S. (2017), {Affine T-S Fuzzy Model-Based Estimation and Control of Hindmarsh-Rose Neuronal Model,} IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2168-2216. %5
  10. [10]  Takagi, T. and Sugeno, M. (1985), {Fuzzy identification of systems and its applications to modeling and control,} IEEE Trans. Syst., Man, Cybern., 15(1), 116-132. %6
  11. [11]  Hua, C.C., Liu, G.P., Li, L., and Guan, X.P. (2018), {Adaptive Fuzzy Prescribed Performance Control for Nonlinear Switched Time-Delay Systems With Unmodeled Dynamics,} IEEE Trans. Fuzzy Syst., 26(4), 1934-1945. %7
  12. [12]  Wu, H.N. and Wang, Z.P. (2018) {Observer-Based $H_1$ Sampled-Data Fuzzy Control for a Class of Nonlinear Parabolic PDE Systems,} IEEE Trans. Fuzzy Syst., 26(2), 454-473. %8
  13. [13]  Parkm, M.J. and Kwon, O.M. (2017), {Stability and stabilization of discrete-time T-S fuzzy systems with time-varying delay via Cauchy?Schwartz-based summation inequality,} IEEE Trans. Fuzzy Syst., 25(1), 128-140. %9
  14. [14]  Lian, Z., He, Y., Zhang, C.K., and Wu, M. (2019), {Stability and stabilization of T-S fuzzy systems with time-varying delays via delay-product type functional method,} IEEE Trans. Cybern., DOI:10.1109/TCYB.2018.2890425. %10
  15. [15]  Peng, C. and Fei, M.R. (2013), {An improved result on the stability of uncertain T-S fuzzy systems with interval time-varying delay,} Fuzzy Sets Syst., 212, 97-109. %11
  16. [16]  Zhao, Y., Gao, H., Lam, J., and Du, B.Z. (2009), {Stability and Stabilization of Delayed T-S Fuzzy Systems: A Delay Partitioning Approach,} IEEE Trans. Fuzz. Sys., 17(4), 750-762. %12
  17. [17]  Zhang, Z.Y., Lin, C., and Chen, B. (2015), {New stability and stabilization conditions for T-S fuzzy systems with time delay,} Fuzzy Sets Syst., 263, 82-91. %13
  18. [18]  Kwon, O.M., Park, M.J., Park, J.H., and Lee, S.M. (2016), {Stability and stabilization of T-S fuzzy systems with time-varying delays via augmented Lyapunov-Krasovskii functionals,} Inf. Sci., 372, 1-15. %14
  19. [19]  Feng, Z.G. and Wei, X.Z. (2017), {Improved Stability Condition for Takagi-Sugeno Fuzzy Systems With Time-Varying Delay,} IEEE Trans. Cybern., 47(3), 661-670. %15
  20. [20]  Wang, Z.P. and Wu, H.N. (2015), {On fuzzy sampled-data control of chaotic systems via a time-dependent Lyapunov functional approach,} IEEE Trans. Cybern., 45(1), 819-829. %16
  21. [21]  Liu, Y. and Lee, S.M. (2016), {Stability and Stabilization of Takagi-Sugeno Fuzzy Systems via Sampled-Data and State Quantized Controller,} IEEE Trans. Fuzzy Syst., 24(3), 635-644. %17
  22. [22]  Liu, Y., Park, J.H., Guo, B., and Shu, Y. (2018), {Further results on stabilization of chaotic systems based on fuzzy memory sampled-data control,} IEEE Trans. Fuzzy Syst., 26(2), 1040-1045. %18
  23. [23]  Zhang, R., Zeng, D., Park, J.H., and Zhong, S. (2018), {A New Approach to Stabilization of Chaotic Systems With Nonfragile Fuzzy Proportional Retarded Sampled-Data Control,} IEEE Trans. Cybern., doi:10.1109/TCYB.2018.2831782. %19
  24. [24]  Wang, Z.P. and Wu, H.N. (2017), {Robust Guaranteed Cost Sampled-Data Fuzzy Control for Uncertain Nonlinear Time-Delay Systems,} IEEE Trans. Syst., Man, Cybern., Syst., DOI:10.1109/TSMC.2017.2703837. %20
  25. [25]  Chen, T. and Francis, B.A. (1995), {Optimal sampled-data control systems,} { Tokyo: SpringerVerlag.} %21
  26. [26]  Kao, C.Y. (2016), {An IQC approach to robust stability of aperiodic sampled data systems,} IEEE Trans. Autom. Control, 61(8), 2219-2225. %22
  27. [27]  Zhang, X.M., Han, Q.L., and Zhang, B.L. (2017), {An overview and deep investigation on sampled-data-based event-triggered control and filtering for networked systems,} IEEE Transactions on Industrial Informatics, 13(1), 4-16. %23
  28. [28]  Zhang, X.M. and Han, Q.L. (2014), {Event-triggered dynamic output feedback control for networked control systems,} IET Control Theory and Applications, 8(4), 226-234. %24
  29. [29]  Liu, K. and Fridman, E. (2012), {Networked-based stabilization via discontinuous Lyapunov functionals,} International Journal of Robust and Nonlinear Control, 22(4), 420-436. %25
  30. [30]  Zeng, H.B., Teo, K.L., He, Y., Xu, H., and Wang, W. (2017), {Sampled-data synchronization control for chaotic neural networks subject to actuator saturation,} Neurocomputing, 260, 25-31. %26
  31. [31]  Zeng, H.B., Teo, K.L., He, Y., and Wang, W. (2019), {Sampled-data-based dissipative control of T-S fuzzy systems,} Applied Mathematical Modelling, 65, 415-427. %27
  32. [32]  Liu, Y., Guo, B.Z., Park, J.H., and Lee, S.M. (2018), {Event-based reliable dissipative filtering for T-S fuzzy systems with asynchronous constraints,} IEEE Transactions on Fuzzy Systems, 26(4), 2089-2098. %28
  33. [33]  Liu, Y., Park, J.H., Guo, B.Z., and Shu, Y. (2018), {Further results on stabilization of chaotic systems based on fuzzy memory sampled-data control,} IEEE Transactions on Fuzzy Systems, 26(2), 1040-1045. %29
  34. [34]  Fujioka, H. (2009), {A discrete-time approach to stability analysis of systems with aperiodic sample-and-hold devices,} IEEE Trans. Autom. Control, 54(10), 2440-2445.
  35. [35]  Zhang, C.K., He, Y., Jiang, L., Wu, M., and Zeng, H.B. (2016), {Delay-variation-dependent stability of delayed discrete-time systems,} IEEE Trans. Autom. Control, 61(9), 2663-2669. %30
  36. [36]  Hu, L., Lam, J., Cao, Y., and Shao, H. (2003), {A LMI approach to robust $H_1$ sampled-data control for linear uncertain systems,} IEEE Trans. Syst., Man, Cybern. B, Cybern., 33(1), 149-155.
  37. [37]  Guan, Z.H., Liu, Z.W., Feng, G., and Wang, Y.W. (2010), {Synchronization of complex dynamical networks with time-varying delays via impulsive distributed Control,} IEEE Trans. Circuits Syst. I Regul. 57, 2182-2195. %31
  38. [38]  Fridman, E. (2010), {A refined input delay approach to sampled-data control,} Automatica, 46(2), 421-427. %32
  39. [39]  Zhu, X.L., Chen, B., Yue, D., and Wang, Y. (2012), {An improved input delay approach to stabilization of fuzzy systems under variable sampling,} IEEE Trans. Fuzz. Syst., 20(2), 330-341. %37
  40. [40]  Zhang, C.K., He, Y., Jiang, L., Wu, M., and Wu, Q.H. (2014), {Stability analysis of sampled-data system considering time delays and its application to electric power markets,} J. Frankl. Inst., 351(9), 4457-4478.
  41. [41]  Seuret, A. (2012), {A novel stability analysis of linear systems under asynchronous samplings,} Automatica, 48(1), 177-182. %39
  42. [42]  Zeng, H.B., Teo, K.L., and He, Y. (2017), {A new looped-functional for stability analysis of sampled-data systems,} Automatica, 328-331. %40
  43. [43]  Seuret, A. and Briat, C. (2015), {Stability analysis of uncertain sampled-data systems with incremental delay using looped-functionals,} Automatica, 55, 274-278. %41 %34
  44. [44]  Liu, K. and Fridman, E. (2012), {Witrtingers inequality and Lyapunov-based sampled-data stabilization,} Automatica, 48(1), 102-108. %35
  45. [45]  Liu, K. and Fridman, E. (2012), {Networked-based Stabilization via discontinuous Lyapunov functional,} Int. J. Robust Nonlinear. Control, 22(4), 420-436. %36
  46. [46]  Zhang, C.K., Jiang, Y., He, L., and Wu, H. (2013), {Stability analysis for control systems with aperiodically sampled data using an augmented Lyapunov functional method,} IET Control Theory Appl., 7(9), 1219-1226. %38
  47. [47]  Zeng, H.B., Zhai, Z.L., Xiao, H.Q., and Wang, W. (2019), {Stability analysis of sampled-data control systems with constant communication delays,} IEEE Access, 7, 111-116.
  48. [48]  Hua, C., Shuangshuang, W., and Guan, X. (2015), {Stabilization of T-S Fuzzy System with Time Delay under Sampled-data Control using A New Looped-Functional,} IEEE Transactions on Fuzzy Systems, 14(8), 1063-6706. %33
  49. [49]  Zeng, X.M., Han, Q.L., Seuret, A., Gouaisbaut, F., and He, Y. (2019), {Overview of resent advances in stability of linear systems with time-varying delays,} IET Control Theory Appl., 13(1), 1-6. %42
  50. [50]  Zeng, H.B., Liu, X.G., and Wang, W. (2019), {A generalized free-matrix-based integral inequality for stability analysis of time-varying delay systems,} Appl. Math. Comput., 354, 1-8.
  51. [51]  Zeng, H.B., He, Y., Wu, M., and She, J. (2015), {Free-matrix-based integral inequality for stability analysis of systems with time-varying delay,} IEEE Trans. Autom. Control, 60(10), 2768-2772.
  52. [52]  Seuret, A. and Gouaisbaut, F. (2013), {Wirtinger-based integral inequality: application TC time-delay systems,} Automatica, 49(9), 2860-2866. %45
  53. [53]  Lakshmanan, S., Lim, C.P., Nahavandi, S., Prakash, M., and Balasubramaniam, P. (2016), {Dynamical Analysis of the Hindmarsh-Rose Neuron with Time Delay,} IEEE Transactions on Neural Networks And Learning Systems, 2162-2379. %46 %44
  54. [54]  Beyhan, S., Lendek, Z., Alci, M., and Babuska, R. (2013), Takagi-sugeno fuzzy observer and extended-Kalman filter for adaptive payload estimation, Proc. 9th Asian Control Conf. (ASCC), Istanbul, Turkey, 1-6. %43
  55. [55]  Seuret, A. and Gouaisbaut, F. (2017), {Stability of Linear Systems With Time-Varying Delays Using Bessel Legendre Inequalities,} IEEE Trans. Autom. Control, 63(1), 225-232.
  56. [56]  Li, X.D. and Cao, J.D. (2017), {An impulsive delay inequality involving unbounded time-varying delay and applications,} IEEE Trans. Autom. Control, 62, 3618-3625.

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