Stabilization control of generalized type neural networks with piecewise constant argument
Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 6, p. 3580-3599.

Voir la notice de l'article provenant de la source International Scientific Research Publications

The generalized type neural networks have always been a hotspot of research in recent years. This paper concerns the stabilization control of generalized type neural networks with piecewise constant argument. Through three types of stabilization control rules (single state stabilization control rule, multiple state stabilization control rule and output stabilization control rule), together with the estimate of the state vector with piecewise constant argument, several succinct criteria of stabilization are derived. The obtained results improve and extend some existing results. Two numerical examples are proposed to substantiate the effectiveness of the theoretical results.
DOI : 10.22436/jnsa.009.06.12
Classification : 34H15, 93D15
Keywords: Generalized type systems, neural networks, state stabilization, output stabilization.

Wan, Liguang 1 ; Wu, Ailong 2

1 College of Mechatronics and Control Engineering, Hubei Normal University, Huangshi 435002, China
2 hbnuwu@yeah.net, Hubei Normal University, Huangshi 435002, China
@article{JNSA_2016_9_6_a11,
     author = {Wan, Liguang and Wu, Ailong},
     title = {Stabilization control of generalized type neural networks with piecewise constant argument},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {3580-3599},
     publisher = {mathdoc},
     volume = {9},
     number = {6},
     year = {2016},
     doi = {10.22436/jnsa.009.06.12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.06.12/}
}
TY  - JOUR
AU  - Wan, Liguang
AU  - Wu, Ailong
TI  - Stabilization control of generalized type neural networks with piecewise constant argument
JO  - Journal of nonlinear sciences and its applications
PY  - 2016
SP  - 3580
EP  - 3599
VL  - 9
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.06.12/
DO  - 10.22436/jnsa.009.06.12
LA  - en
ID  - JNSA_2016_9_6_a11
ER  - 
%0 Journal Article
%A Wan, Liguang
%A Wu, Ailong
%T Stabilization control of generalized type neural networks with piecewise constant argument
%J Journal of nonlinear sciences and its applications
%D 2016
%P 3580-3599
%V 9
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.06.12/
%R 10.22436/jnsa.009.06.12
%G en
%F JNSA_2016_9_6_a11
Wan, Liguang; Wu, Ailong. Stabilization control of generalized type neural networks with piecewise constant argument. Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 6, p. 3580-3599. doi : 10.22436/jnsa.009.06.12. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.06.12/

[1] Akhmet, M. U. On the reduction principle for differential equations with piecewise constant argument of generalized type, J. Math. Anal. Appl., Volume 336 (2007), pp. 646-663

[2] Akhmet, M. U. Almost periodic solutions of differential equations with piecewise constant argument of generalized type, Nonlinear Anal. Hybrid Syst., Volume 2 (2008), pp. 456-467

[3] Akhmet, M. U. Stability of differential equations with piecewise constant arguments of generalized type, Nonlinear Anal., Volume 68 (2008), pp. 794-803

[4] Akhmet, M. U.; Arugaslan, D. Lyapunov-Razumikhin method for differential equations with piecewise constant argument, Discrete Contin. Dyn. Syst, Volume 25 (2009), pp. 457-466

[5] Akhmet, M. U.; Arugaslan, D.; Yılmaz, E. Stability analysis of recurrent neural networks with piecewise constant argument of generalized type, Neural Netw., Volume 23 (2010), pp. 805-811

[6] Akhmet, M. U.; Arugaslan, D.; Yımlaz, E. Stability in cellular neural networks with piecewise constant argument, J. Comput. Appl. Math., Volume 233 (2010), pp. 2365-2373

[7] Akhmet, M. U.; Yımlaz, E. Impulsive Hopfield-type neural network system with piecewise constant argument, Nonlinear Anal. Real World Appl., Volume 11 (2010), pp. 2584-2593

[8] Balasubramaniam, P.; G. Nagamani Passivity analysis of neural networks with Markovian jumping parameters and interval time-varying delays, Nonlinear Anal. Hybrid Syst., Volume 4 (2010), pp. 853-864

[9] Bao, G.; Wen, S. P.; Zeng, Z. G. Robust stability analysis of interval fuzzy Cohen-Grossberg neural networks with piecewise constant argument of generalized type, Neural Netw., Volume 33 (2012), pp. 32-41

[10] Chen, W. H.; Lu, X. M.; Guan, Z. H.; Zheng, W. X. Delay-dependent exponential stability of neural networks with variable delay: an LMI approach, IEEE Trans. Circuit Syst. II Expr. Bri., Volume 53 (2006), pp. 837-842

[11] Chen, W. H.; Lu, X. M.; Zhen, W. X. Impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks, IEEE Trans. Neural Netw. Learn Syst., Volume 26 (2015), pp. 734-748

[12] Chen, W. H.; Luo, S. X. Multistability in a class of stochastic delayed Hopfield neural networks, Neural Netw., Volume 68 (2015), pp. 52-61

[13] Fourati, F.; Chtourou, M.; Kamoun, M. Stabilization of unknown nonlinear systems using neural networks, Appl. Soft Comput., Volume 8 (2008), pp. 1121-1130

[14] Guo, Z. Y.; Wang, J. Global exponential synchronization of two memristor-baesd recurrent neural networks with time delays via static or dynamic coupling, IEEE Trans. Syst., Man, Cybern. B., Cybern, Volume 45 (2015), pp. 235-249

[15] Hua, C.; Guan, X. Output feedback stabilization for time-delay nonlinear interconnected systems using neural networks, IEEE Trans. Neural Netw., Volume 19 (2008), pp. 673-688

[16] Huang, T. W. Exponential stability of fuzzy cellular neural networks with distributed delay, Phys. Lett. A., Volume 351 (2006), pp. 48-52

[17] Huang, C. X.; Cao, J. Convergence dynamics of stochastic Cohen-Crossberg neural networks with unbounded distributed delays, IEEE Trans. Neural Netw., Volume 22 (2011), pp. 561-572

[18] Kaslik, E.; Sivasundaram, S. Impulsive hybrid discrete-time Hopfield neural networks with delays and multistability analysis, Neural Netw., Volume 24 (2011), pp. 370-377

[19] Li, T.; Song, A. G.; Fei, S. M.; Wang, T. Delay-derivative-dependent stability for delayed neural networks with unbounded distributed delay, IEEE Trans. Neural Netw., Volume 21 (2010), pp. 1365-1371

[20] Li, C. D.; C.Wu, S.; Feng, G. G.; Liao, X. F. Stabilizing effects of impulses in discrete-time delayed neural networks, IEEE Trans. Neural Netw., Volume 22 (2011), pp. 323-329

[21] Liao, X. F.; Chen, G.; Sanchez, E. N. Delay-dependent exponential stability analysis of delayed neural networks: An LMI approach, Neural Netw., Volume 15 (2002), pp. 855-866

[22] Liu, Z. Q.; Torres, R. E.; Patel, N.; Wang, Q. J. Further development of input-to-state stabilizing control for dynamic neural network systems, IEEE Trans. Syst. Man Cybern. A., Volume 38 (2008), pp. 1425-1433

[23] Long, F.; S. M. Fei Neural networks stabilization and disturbance attenuation for nonlinear switched impulsive systems, Neurocomputing, Volume 71 (2008), pp. 1741-1747

[24] Patan, K. Stability analysis and the stabilization of a class of discretetime dynamic neural networks, IEEE Trans. Neural Netw, Volume 18 (2007), pp. 660-673

[25] Phat, V. N.; H. Trinh Exponential stabilization of neural networks with various activation functions and mixed time-varying delays, IEEE Trans. Neural Netw., Volume 21 (2010), pp. 1180-1184

[26] Shen, Y.; J. Wang Noise-induced stabilization of the recurrent neural networks with mixed time-varying delays and Markovian-switching parameters, IEEE Trans. Neural Netw, Volume 18 (2007), pp. 1857-1862

[27] Shen, Y.; Wang, J. Robustness analysis of global exponential stability of recurrent neural networks in the presence of time delays and random disturbances, IEEE Trans. Neural Netw. Learn Syst., Volume 23 (2012), pp. 87-96

[28] Song, Q. K.; Cao, J. Passivity of uncertain neural networks with both leakage delay and time-varying delay, Nonlinear Dyn., Volume 67 (2012), pp. 1695-1707

[29] Wu, A. L.; Zeng, Z. G. Exponential stabilization of memristive neural networks with time delays, IEEE Trans. Neural Netw. Learn Syst., Volume 23 (2012), pp. 1919-1929

[30] Wu, A. L.; Z. G. Zeng Lagrange stability of memristive neural networks with discrete and distributed delays, IEEE Trans. Neural Netw. Learn Syst., Volume 25 (2014), pp. 690-703

[31] Wu, A. L.; Zeng, Z. G. New global exponential stability results for memristive neural system with time-varying delays, Neurocomputing, Volume 144 (2014), pp. 553-559

[32] Xiao, J.; Zeng, Z. G.; Wen, S. P.; Wu, A. L. Passivity analysis of delayed neural networks with discontinuous activations via differential inclusions, Nonlinear Dyn., Volume 74 (2013), pp. 213-225

[33] Zeng, Z. G.; Huang, D. S. Pattern memory analysis based on stability theory of cellular neural networks, Appl. Math. Model., Volume 32 (2008), pp. 112-121

[34] Zeng, Z. G.; Wang, J. Global exponential stability of recurrent neural networks with time-varying delays in the presence of strong external stimuli , Neural Netw., Volume 19 (2006), pp. 1528-1537

[35] Zeng, Z. G.; Zheng, W. X. Multistability of two kinds of recurrent neural networks with activation funtions symmetrical about the origin on the phase plane, IEEE Trans Neural Netw Learn Syst., Volume 24 (2013), pp. 1749-1762

[36] Zhang, Z. Y.; Lin, C.; Chen, B. Global stability criterion for delayed complex-valued recurrent neural networks, IEEE Trans. Neural Netw. Learn Syst., Volume 25 (2014), pp. 1704-1708

[37] Zhu, X. L.; Y. Y. Wang Stabilization for sampled-data neural-network-based control systems, IEEE Trans. Syst., Man, Cybern B., Cybern, Volume 41 (2011), pp. 210-221

Cité par Sources :