| Title:
|
Existence, uniqueness and global asymptotic stability for a class of complex-valued neutral-type neural networks with time delays (English) |
| Author:
|
Tan, Manchun |
| Author:
|
Xu, Desheng |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
54 |
| Issue:
|
4 |
| Year:
|
2018 |
| Pages:
|
844-863 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper explores the problem of delay-independent and delay-dependent stability for a class of complex-valued neutral-type neural networks with time delays. Aiming at the neutral-type neural networks, an appropriate function is constructed to derive the existence of equilibrium point. On the basis of homeomorphism theory, Lyapunov functional method and linear matrix inequality techniques, several LMI-based sufficient conditions on the existence, uniqueness and global asymptotic stability of equilibrium point for complex-valued neutral-type neural networks are obtained. Finally, numerical examples are given to illustrate the feasibility and the effectiveness of the proposed theoretical results. (English) |
| Keyword:
|
complex-valued neutral-type neural networks |
| Keyword:
|
existence and uniqueness of equilibrium |
| Keyword:
|
global asymptotic stability |
| Keyword:
|
inequality techniques |
| Keyword:
|
Lyapunov functional |
| MSC:
|
37B25 |
| MSC:
|
92B20 |
| idZBL:
|
Zbl 06987038 |
| idMR:
|
MR3863260 |
| DOI:
|
10.14736/kyb-2018-4-0844 |
| . |
| Date available:
|
2018-11-02T10:31:42Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147440 |
| . |
| Reference:
|
[1] Boyd, S., Ghaoui, L. E., Feron, E., Balakrishnam, V.: Linear Matrix Inequality in System and Control..SIAM, Philadelphia, 1994. 10.1137/1.9781611970777 |
| Reference:
|
[2] Cao, J. D., Chen, G. R., Li, P.: Global synchronization in an array of delayed neural networks with hybrid coupling..IEEE Trans. Syst. Man Cybern. B 38 (2008), 2, 488-498. 10.1109/tsmcb.2007.914705 |
| Reference:
|
[3] Chen, X. F., Song, Q. K.: Global stability of complex-valued neural networks with both leakage time delay and discrete time delay on time scales..Neurocomputing 121 (2013), 254-264. 10.1016/j.neucom.2013.04.040 |
| Reference:
|
[4] Ding, X. S., Cao, J. D., Alsaedi, A., Alsaadi, F. E., Hayat, T.: Robust fixed-time synchronization for uncertain complex-valued neural networks with discontinuous activation functions..Neural Netw. 90 (2017), 42-55. 10.1016/j.neunet.2017.03.006 |
| Reference:
|
[5] Du, B., Liu, Y., Cao, J. D.: Stability analysis for neutral-type impulsive neural networks with delays..Kybernetika 53 (2017), 3, 513-529. MR 3684683, 10.14736/kyb-2017-3-0513 |
| Reference:
|
[6] Fang, T., Sun, J. T.: Further investigate the stability of complex-valued recurrent neural networks with time-delays..IEEE Trans. Neural Netw. Learn. Syst. 25 (2014), 9, 1709-1713. MR 3453740, 10.1109/tnnls.2013.2294638 |
| Reference:
|
[7] Fang, T., Sun, J. T.: Stability of complex-valued impulsive and switching system and application to the Lu system..Nonlinear Anal. Hybrid Syst. 14 (2014), 38-46. MR 3228049, 10.1016/j.nahs.2014.04.004 |
| Reference:
|
[8] Feng, J. E., Xu, S. Y., Zou, Y.: Delay-dependent stability of neutral type neural networks with distributed delays..Neurocomputing 72 (2009), 10-12, 2576-2580. 10.1016/j.neucom.2008.10.018 |
| Reference:
|
[9] Forti, M., Tesi, A.: New conditions for global stability of neural networks with application to linear and quadratic programming problems..IEEE Trans. Circuits Syst. I 42 (1995), 354-366. MR 1351871, 10.1109/81.641813 |
| Reference:
|
[10] Gong, W. Q., Liang, J. L., Zhang, C. J., Cao, J. D.: Nonlinear measure approach for the stability analysis of complex-valued neural networks..Neural Process. Lett. 44 (2015), 539-554. 10.1007/s11063-015-9475-9 |
| Reference:
|
[11] Guo, R. N., Zhang, Z. Y., Liu, X. P., Lin, C.: Existence, uniqueness, and exponential stability analysis for complex-valued memristor-based BAM neural networks with time delays..Appl. Math. Comput. 311 (2017), 100-117. MR 3658062, 10.1016/j.amc.2017.05.021 |
| Reference:
|
[12] Hirose, A.: Complex-Valued Neural Networks: Theories and Applications..World Scientific, Singapore 2003. MR 2061862, 10.1142/9789812791184 |
| Reference:
|
[13] Hirose, A.: Recent progress in applications of complex-valued neural networks..In: Artif. Intell. Soft. Comput. II, Vol. 6114 (L. Rutkowski et al., eds.), Springer, New York 2010, pp. 42-46. 10.1007/978-3-642-13232-2\_6 |
| Reference:
|
[14] Hu, J., Wang, J.: Global stability of complex-valued recurrent neural networks with time-delays..IEEE Trans. Neural Netw. Learn. Syst. 23 (2012), 6, 853-865. MR 3453740, 10.1109/tnnls.2012.2195028 |
| Reference:
|
[15] Liao, X. F., Liu, Y. L., Wang, H. W., Huang, T. W.: Exponential estimates and exponential stability for neutral-type neural networks with multiple delays..Neurocomputing 149 (2015), 868-883. MR 3593044, 10.1016/j.neucom.2014.07.048 |
| Reference:
|
[16] Liu, X. W., Chen, T. P.: Global Exponential stability for complex-valued recurrent neural networks with asynchronous time delays..IEEE Trans. Neural Netw. Learn. Syst. 27 (2016), 3, 593-606. MR 3465659, 10.1109/tnnls.2015.2415496 |
| Reference:
|
[17] Pan, J., Liu, X. Z., Xie, W. C.: Exponential stability of a class of complex-valued neural networks with time-varying delays..Neurocomputing 164 (2015), 293-299. 10.1016/j.neucom.2015.02.024 |
| Reference:
|
[18] Orman, Z.: New sufficient conditions for global stability of neutral-type neural networks with time delays..Neurocomputing 97 (2012), 141-148. 10.1016/j.neucom.2012.05.016 |
| Reference:
|
[19] Patan, K.: Stability analysis and the stabilization of a class of discrete-time dynamic neural networks..IEEE Trans. Neural Netw. 18 (2007), 3, 660-673. 10.1109/tnn.2007.891199 |
| Reference:
|
[20] Park, J. H., Kwon, O. M.: Further results on state estimation for neural networks of neutral-type with time-varying delay..Appl. Math. Comput. 208 (2009), 1, 69-75. MR 2490770, 10.1016/j.amc.2008.11.017 |
| Reference:
|
[21] Park, J. H., Kwon, O. M., Lee, S. M.: LMI optimization approach on stability for delayed neural networks of neutral-type..Appl. Math. Comput. 196 (2008), 1, 236-244. MR 2382607, 10.1016/j.amc.2007.05.047 |
| Reference:
|
[22] Park, J. H., Park, C. H., Kwon, O. M., Lee, S. M.: A new stability criterion for bidirectional associative memory neural networks of neutral-type..Appl. Math. Comput. 199 (2008), 2, 716-722. MR 2420599, 10.1016/j.amc.2007.10.032 |
| Reference:
|
[23] Shi, K. B., Zhong, S. M., Zhu, H., Liu, X. Z., Zeng, Y.: New delay-dependent stability criteria for neutral-type neural networks with mixed random time-varying delays..Neurocomputing 168 (2015), 896-907. MR 3402310, 10.1016/j.neucom.2015.05.035 |
| Reference:
|
[24] Shu, Y.J., Liu, X.G., Wang, F.X., Qiu, S.B.: Further results on exponential stability of discrete-time BAM neural networks with time-varying delays..Math. Method. Appl. Sci. 40 (2017), 11, 4014-4027. MR 3668827, 10.1002/mma.4281 |
| Reference:
|
[25] Song, Q. K.: Synchronization analysis of coupled connected neural networks with mixed time delays..Neurocomputing 72 (2009), 3907-3914. 10.1016/j.neucom.2009.04.009 |
| Reference:
|
[26] Song, Q. K., Shu, H. Q., Zhao, Z. J., Liu, Y. R., Alsaadi, F. E.: Lagrange stability analysis for complex-valued neural networks with leakage delay and mixed time-varying delays..Neurocomputing 244 (2017), 33-41. 10.1016/j.neucom.2017.03.015 |
| Reference:
|
[27] Song, Q. K., Yan, H., Zhao, Z. J., Liu, Y. R.: Global exponential stability of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays..Neural Netw. 81 (2016), 1-10. 10.1016/j.neunet.2016.04.012 |
| Reference:
|
[28] Song, Q. K., Zhao, Z. J., Liu, Y. R.: Stability analysis of complex-valued neural networks with probabilistic time-varying delays..Neurocomputing 159 (2015), 96-104. 10.1016/j.neucom.2015.02.015 |
| Reference:
|
[29] Subramanian, K., Muthukumar, P.: Global asymptotic stability of complex-valued neural networks with additive time-varying delays..Cogn. Neurodynamics 11 (2017), 3, 293-306. 10.1007/s11571-017-9429-1 |
| Reference:
|
[30] Tan, M. C.: Global asymptotic stability of fuzzy cellular neural networks with unbounded distributed delays..Neural Process. Lett. 31 (2010), 2, 147-157. 10.1007/s11063-010-9130-4 |
| Reference:
|
[31] Tan, M. C.: Stabilization of coupled time-delay neural networks with nodes of different dimensions..Neural Process. Lett. 43 (2016), 1, 255-268. 10.1007/s11063-015-9416-7 |
| Reference:
|
[32] Tan, Y. X., Jing, K.: Existence and global exponential stability of almost periodic solution for delayed competitive neural networks with discontinuous activations..Math. Method. Appl. Sci. 39 (2016), 11, 2821-2839. MR 3512733, 10.1002/mma.3732 |
| Reference:
|
[33] Tan, M. C., Xu, D. S.: Multiple $\mu$-stability analysis for memristor-based complex-valued neural networks with nonmonotonic piecewise nonlinear activation functions and unbounded time-varying delays..Neurocomputing 275 (2018), 2681-2701. 10.1016/j.neucom.2017.10.038 |
| Reference:
|
[34] Tan, M. C., Zhang, Y. N.: New sufficient conditions for global asymptotic stability of Cohen-Grossberg neural networks with time-varying delays..Nonlinear Anal. Real World Appl. 10 (2009), 2139-2145. MR 2508424, 10.1016/j.nonrwa.2008.03.022 |
| Reference:
|
[35] Tian, X. H., Xu, R.: Stability and Hopf bifurcation of a delayed Cohen-Grossberg neural network with diffusion..Math. Method. Appl. Sci. 40 (2017), 1, 293-305. MR 3583055, 10.1002/mma.3995 |
| Reference:
|
[36] Tu, Z. W., Cao, J. D., Alsaedi, A., Alsaadi, F. E., Hayat, T.: Global lagrange stability of complex-valued neural networks of neutral type with time-varying delays..Complexity 21 (2016), S2, 438-450. MR 3583097, 10.1002/cplx.21823 |
| Reference:
|
[37] Wang, H. M., Duan, S. K., Huang, T. W., Wang, L. D., Li, C. D.: Exponential stability of complex-valued memristive recurrent neural networks..IEEE Trans. Neural Netw. Learn. Syst. 28 (2017), 3, 766-771. MR 3730910, 10.1109/TNNLS.2015.2513001 |
| Reference:
|
[38] Wang, Z. Y., Huang, L. H.: Global stability analysis for delayed complex-valued BAM neural networks..Neurocomputing 173 (2016), 2083-2089. 10.1016/j.neucom.2015.09.086 |
| Reference:
|
[39] Wang, P., Li, Y. K., Ye, Y.: Almost periodic solutions for neutral-type neural networks with the delays in the leakage term on time scales..Math. Method. Appl. Sci. 39 (2016), 15, 4297-4310. MR 3549393, 10.1002/mma.3857 |
| Reference:
|
[40] Wang, L., Xie, Y., Wei, Z., Peng, J.: Stability analysis and absolute synchronization of a three-unit delayed neural network..Kybernetika 51 (2015), 5, 800-813. MR 3445985, 10.14736/kyb-2015-5-0800 |
| Reference:
|
[41] Xie, J., Kao, Y. G., Park, J.H.: $H_\infty$ performance for neutral-type Markovian switching systems with general uncertain transition rates via sliding mode control method..Nonlinear Anal. Hybrid Syst. 27 (2018), 416-436. MR 3729580, 10.1016/j.nahs.2017.10.002 |
| Reference:
|
[42] Xu, C. J., Li, P. L., Pang, Y. C.: Existence and exponential stability of almost periodic solutions for neutral-type BAM neural networks with distributed leakage delays..Math. Method. Appl. Sci. 40 (2017), 6, 2177-2196. MR 3624090, 10.1002/mma.4132 |
| Reference:
|
[43] Xu, X. H., Zhang, J. Y., Shi, J. Z.: Exponential stability of complex-valued neural networks with mixed delays..Neurocomputing 128 (2014), 483-490. 10.1016/j.neucom.2013.08.014 |
| Reference:
|
[44] Zhang, H. G., Gong, D. W., Wang, Z. S.: Synchronization criteria for an array of neutral-type neural networks with hybrid coupling: a novel analysis approach..Neural Process. Lett. 35 (2012), 1, 29-45. 10.1007/s11063-011-9202-0 |
| Reference:
|
[45] Zhang, Z. Y., Liu, X. P., Chen, J., Guo, R. N., Zhou, S. W.: Further stability analysis for delayed complex-valued recurrent neural networks..Neurocomputing 251 (2017), 81-89. 10.1016/j.neucom.2017.04.013 |
| Reference:
|
[46] Zhang, Z. Y., Lin, C., Chen, B.: Global stability criterion for delayed complex-valued recurrent neural networks..IEEE Trans. Neural Netw. Learn. Syst. 25 (2014), 9, 1704-1708. 10.1109/tnnls.2013.2288943 |
| Reference:
|
[47] Zhang, Z. Q., Yu, S. H.: Global asymptotic stability for a class of complex-valued Cohen-Grossberg neural networks with time delays..Neurocomputing 171 (2016), 1158-1166. 10.1016/j.neucom.2015.07.051 |
| Reference:
|
[48] Zeng, X., Li, C. D., Huang, T. W., He, X.: Stability analysis of complex-valued impulsive systems with time delay..Appl. Math. Comput. 256 (2015), 75-82. MR 3316049, 10.1016/j.amc.2015.01.006 |
| Reference:
|
[49] Zheng, C. D., Shan, Q. H., Zhang, H. G.: On stabilization of stochastic Cohen-Grossberg neural networks with mode-dependent mixed time-delays and Markovian switching..IEEE Trans. Neural Netw. Learn. Syst. 24 (2013), 800-811. 10.1109/tnnls.2013.2244613 |
| . |
