Stabilization control of generalized type neural networks with piecewise constant argument
-
2132
Downloads
-
3892
Views
Authors
Liguang Wan
- College of Mechatronics and Control Engineering, Hubei Normal University, Huangshi 435002, China.
Ailong Wu
- hbnuwu@yeah.net, Hubei Normal University, Huangshi 435002, China.
Abstract
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.
Share and Cite
ISRP Style
Liguang Wan, Ailong Wu, Stabilization control of generalized type neural networks with piecewise constant argument, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 3580--3599
AMA Style
Wan Liguang, Wu Ailong, Stabilization control of generalized type neural networks with piecewise constant argument. J. Nonlinear Sci. Appl. (2016); 9(6):3580--3599
Chicago/Turabian Style
Wan, Liguang, Wu, Ailong. "Stabilization control of generalized type neural networks with piecewise constant argument." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 3580--3599
Keywords
- Generalized type systems
- neural networks
- state stabilization
- output stabilization.
MSC
References
-
[1]
M. U. Akhmet, On the reduction principle for differential equations with piecewise constant argument of generalized type, J. Math. Anal. Appl., 336 (2007), 646–663.
-
[2]
M. U. Akhmet, Almost periodic solutions of differential equations with piecewise constant argument of generalized type, Nonlinear Anal. Hybrid Syst., 2 (2008), 456–467.
-
[3]
M. U. Akhmet, Stability of differential equations with piecewise constant arguments of generalized type, Nonlinear Anal., 68 (2008), 794–803.
-
[4]
M. U. Akhmet, D. Arugaslan, Lyapunov-Razumikhin method for differential equations with piecewise constant argument, Discrete Contin. Dyn. Syst, 25 (2009), 457–466.
-
[5]
M. U. Akhmet, D. Arugaslan, E. Yılmaz, Stability analysis of recurrent neural networks with piecewise constant argument of generalized type, Neural Netw., 23 (2010), 805–811.
-
[6]
M. U. Akhmet, D. Arugaslan, E. Yımlaz, Stability in cellular neural networks with piecewise constant argument, J. Comput. Appl. Math., 233 (2010), 2365–2373.
-
[7]
M. U. Akhmet, E. Yımlaz, Impulsive Hopfield-type neural network system with piecewise constant argument, Nonlinear Anal. Real World Appl., 11 (2010), 2584–2593.
-
[8]
P. Balasubramaniam, G. Nagamani , Passivity analysis of neural networks with Markovian jumping parameters and interval time-varying delays, Nonlinear Anal. Hybrid Syst., 4 (2010), 853–864.
-
[9]
G. Bao, S. P. Wen, Z. G. Zeng, Robust stability analysis of interval fuzzy Cohen-Grossberg neural networks with piecewise constant argument of generalized type, Neural Netw., 33 (2012), 32–41.
-
[10]
W. H. Chen, X. M. Lu, Z. H. Guan, W. X. Zheng, Delay-dependent exponential stability of neural networks with variable delay: an LMI approach, IEEE Trans. Circuit Syst. II Expr. Bri., 53 (2006), 837–842.
-
[11]
W. H. Chen, X. M. Lu, W. X. Zhen, Impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks, IEEE Trans. Neural Netw. Learn Syst., 26 (2015), 734–748.
-
[12]
W. H. Chen, S. X. Luo, Multistability in a class of stochastic delayed Hopfield neural networks, Neural Netw., 68 (2015), 52–61.
-
[13]
F. Fourati, M. Chtourou, M. Kamoun, Stabilization of unknown nonlinear systems using neural networks, Appl. Soft Comput., 8 (2008), 1121–1130.
-
[14]
Z. Y. Guo, J. Wang, 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, 45 (2015), 235–249.
-
[15]
C. Hua, X. Guan, Output feedback stabilization for time-delay nonlinear interconnected systems using neural networks, IEEE Trans. Neural Netw., 19 (2008), 673–688.
-
[16]
T. W. Huang, Exponential stability of fuzzy cellular neural networks with distributed delay, Phys. Lett. A., 351 (2006), 48–52.
-
[17]
C. X. Huang, J. Cao, Convergence dynamics of stochastic Cohen-Crossberg neural networks with unbounded distributed delays, IEEE Trans. Neural Netw., 22 (2011), 561–572.
-
[18]
E. Kaslik, S. Sivasundaram, Impulsive hybrid discrete-time Hopfield neural networks with delays and multistability analysis, Neural Netw., 24 (2011), 370–377.
-
[19]
T. Li, A. G. Song, S. M. Fei, T. Wang, Delay-derivative-dependent stability for delayed neural networks with unbounded distributed delay, IEEE Trans. Neural Netw., 21 (2010), 1365–1371.
-
[20]
C. D. Li, S. C.Wu, G. G. Feng, X. F. Liao, Stabilizing effects of impulses in discrete-time delayed neural networks, IEEE Trans. Neural Netw., 22 (2011), 323–329.
-
[21]
X. F. Liao, G. Chen, E. N. Sanchez, Delay-dependent exponential stability analysis of delayed neural networks: An LMI approach, Neural Netw., 15 (2002), 855–866.
-
[22]
Z. Q. Liu, R. E. Torres, N. Patel, Q. J. Wang, Further development of input-to-state stabilizing control for dynamic neural network systems, IEEE Trans. Syst. Man Cybern. A., 38 (2008), 1425–1433.
-
[23]
F. Long, S. M. Fei , Neural networks stabilization and disturbance attenuation for nonlinear switched impulsive systems, Neurocomputing, 71 (2008), 1741–1747.
-
[24]
K. Patan, Stability analysis and the stabilization of a class of discretetime dynamic neural networks, IEEE Trans. Neural Netw, 18 (2007), 660–673.
-
[25]
V. N. Phat, H. Trinh , Exponential stabilization of neural networks with various activation functions and mixed time-varying delays, IEEE Trans. Neural Netw., 21 (2010), 1180–1184.
-
[26]
Y. Shen, J. Wang , Noise-induced stabilization of the recurrent neural networks with mixed time-varying delays and Markovian-switching parameters, IEEE Trans. Neural Netw, 18 (2007), 1857–1862.
-
[27]
Y. Shen, J. Wang, 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., 23 (2012), 87–96.
-
[28]
Q. K. Song, J. Cao, Passivity of uncertain neural networks with both leakage delay and time-varying delay, Nonlinear Dyn., 67 (2012), 1695–1707.
-
[29]
A. L. Wu, Z. G. Zeng, Exponential stabilization of memristive neural networks with time delays, IEEE Trans. Neural Netw. Learn Syst., 23 (2012), 1919–1929.
-
[30]
A. L. Wu, Z. G. Zeng , Lagrange stability of memristive neural networks with discrete and distributed delays, IEEE Trans. Neural Netw. Learn Syst., 25 (2014), 690–703.
-
[31]
A. L. Wu, Z. G. Zeng, New global exponential stability results for memristive neural system with time-varying delays, Neurocomputing, 144 (2014), 553–559.
-
[32]
J. Xiao, Z. G. Zeng, S. P. Wen, A. L. Wu, Passivity analysis of delayed neural networks with discontinuous activations via differential inclusions, Nonlinear Dyn., 74 (2013), 213–225.
-
[33]
Z. G. Zeng, D. S. Huang, Pattern memory analysis based on stability theory of cellular neural networks, Appl. Math. Model., 32 (2008), 112–121.
-
[34]
Z. G. Zeng, J. Wang, Global exponential stability of recurrent neural networks with time-varying delays in the presence of strong external stimuli , Neural Netw., 19 (2006), 1528–1537.
-
[35]
Z. G. Zeng, W. X. Zheng, 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., 24 (2013), 1749–1762.
-
[36]
Z. Y. Zhang, C. Lin, B. Chen, Global stability criterion for delayed complex-valued recurrent neural networks, IEEE Trans. Neural Netw. Learn Syst., 25 (2014), 1704–1708.
-
[37]
X. L. Zhu, Y. Y. Wang , Stabilization for sampled-data neural-network-based control systems, IEEE Trans. Syst., Man, Cybern B., Cybern, 41 (2011), 210–221.