Global μ-Stability of Impulsive Complex-Valued Neural Networks With Mixed Time-Varying Delays

YAN Huan; ZHAO Zhen-jiang; SONG Qian-kun

doi:10.3879/j.issn.1000-0887.2015.07.008

Volume 36 Issue 7

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2015 > 36(7): 756-767

YAN Huan, ZHAO Zhen-jiang, SONG Qian-kun. Global μ-Stability of Impulsive Complex-Valued Neural Networks With Mixed Time-Varying Delays[J]. Applied Mathematics and Mechanics, 2015, 36(7): 756-767. doi: 10.3879/j.issn.1000-0887.2015.07.008

Citation:

PDF( 622 KB)

Global μ-Stability of Impulsive Complex-Valued Neural Networks With Mixed Time-Varying Delays

doi: 10.3879/j.issn.1000-0887.2015.07.008

¹School of Information Science and Engineering, Chongqing Jiaotong University, Chongqing 400074, P.R.China;²Department of Mathematics, Huzhou University, Huzhou, Zhejiang 313000, P.R.China;³Department of Mathematics, Chongqing Jiaotong University, Chongqing 400074, P.R.China

Funds: The National Natural Science Foundation of China(61273021; 61473332)

Received Date: 2015-03-30
Rev Recd Date: 2015-06-10
Publish Date: 2015-07-15

Abstract

Abstract

The global μ-stability of impulsive complex-valued neural networks with mixed time-varying delays was investigated. For the considered complex-valued neural networks, the activation functions only need to satisfy the Lipschitz conditions. Based on the homeomorphism mapping principle in the complex domain, a sufficient condition for the existence and uniqueness of the equilibrium point of the addressed complex-valued neural network was proposed in terms of linear matrix inequalities (LMIs). Through construction of appropriate Lyapunov-Krasovskii functionals, and with the free weighting matrix method and inequality technique, a delay-dependent criterion for checking the global μ-stability of the complex-valued neural networks was established in terms of LMIs. Finally, a simulation example was given to show the effectiveness of the obtained results.
- complex-valued neural network,
- impulsive,
- time-varying delay,
- global μ-stability

FullText(HTML)

References(20)

References

[1]	廖晓昕. Hopfield型神经网络的稳定性[J]. 中国科学（A辑）, 1993,23(10): 1025-1035.(LIAO Xiao-xin. Stability of Hopfield neural networks[J]. Scientia Sinica Mathematica,1993,23(10): 1025-1035.(in Chinese))
[2]	曹进德. 时滞细胞神经网络指数稳定性与周期解[J]. 中国科学（E辑）, 2000,30(3): 328-336.(CAO Jin-de. Exponential stability and periodic solutions of delayed celluar neural networks[J]. Scientia Sinica Technologica,2000,30(3): 328-336(in Chinese))
[3]	SONG Qian-kun. Exponential stability of recurrent neural networks with both time-varying delays and general activation functions via LMI approach[J]. Neurocomputing,2008,71(13/15): 2823-2830.
[4]	LIU Yu-rong, WANG Zi-dong, LIU Xiao-hui. Asymptotic stability for neural networks with mixed time delays: the discrete-time case[J]. Neural Networks,2009,22(1): 67-74.
[5]	Gopalsamy K. Stability of artificial neural networks with impulses[J]. Applied Mathematics and Computation,2004,154(3): 783-813.
[6]	XU Dao-yi, YANG Zhi-chun. Impulsive delay differential inequality and stability of neural networks[J]. Journal of Mathematical Analysis and Applications,2005,305(1): 107-120.
[7]	SONG Qian-kun, ZHANG Ji-ye. Global exponential stability of impulsive Cohen-Grossberg neural network with time-varying delays[J]. Nonlinear Analysis: Real World Applications,2008,9(2): 500-510.
[8]	Rakkiyappan R, Balasubramaniam P, CAO Jin-de. Global exponential stability results for neutral-type impulsive neural networks[J]. Nonlinear Analysis: Real World Applications,2010,11(1): 122-130.
[9]	Tojtovska B, Jankovic S. General decay stability analysis of impulsive neural networks with mixed time delays[J]. Neurocomputing,2014,142: 438-446.
[10]	Hirose A. Complex-Valued Neural Networks: Theories and Applications[M]. Singapore: World Scientific, 2003.
[11]	Lee D L. Relaxation of the stability condition of the complex-valued neural networks[J]. IEEE Transactions on Neural Networks,2001,12(5): 1260-1262.
[12]	Rao V S H, Murthy G R S. Global dynamics of a class of complex valued neural networks[J]. International Journal of Neural Systems,2008,18(2): 165-171.
[13]	ZHOU Wei, Zurada J M. Discrete-time recurrent neural networks with complex-valued linear threshold neurons[J]. IEEE Transactions on Circuits and Systems II: Express Briefs,2009,56(8): 669-673.
[14]	DUAN Cheng-jun, SONG Qian-kun. Boundedness and stability for discrete-time delayed neural network with complex-valued linear threshold neurons[J]. Discrete Dynamics in Nature and Society,2010,2010: 368379. doi: 10.1155/2010/368379.
[15]	HU Jin, WANG Jun. Global stability of complex-valued recurrent neural networks with time-delays[J]. IEEE Transactions on Neural Networks and Learning Systems,2012,23(6): 853-865.
[16]	ZHOU Bo, SONG Qian-kun. Boundedness and complete stability of complex-valued neural networks with time delay[J]. IEEE Transactions on Neural Networks and Learning Systems,2013,24(8): 1227-1238.
[17]	Rakkiyappan R, Velmurugan G, LI Xiao-di. Complete stability analysis of complex-valued neural networks with time delays and impulses[J]. Neural Processing Letters,2015,41(3): 435-468. doi: 10.1007/s11063-014-9349-6.
[18]	CHEN Xiao-feng, SONG Qian-kun, LIU Xiao-hui, ZHAO Zhen-jiang. Global μ-stability of complex-valued neural networks with unbounded time-varying delays[J]. Abstract and Applied Analysis Volume,2014,2014. doi: 10.1155/2014/263847.
[19]	CHEN Xiao-feng, SONG Qian-kun, LUI Yu-rong, ZHAO Zhen-jiang. Global μ-stability of impulsive complex-valued neural networks with leakage delay and mixed delays[J]. Abstract and Applied Analysis Volume,2014,2014. doi: 10.1155/2014/397532.
[20]	CHEN Tian-ping, WANG Li-li. Global μ-stability of delayed neural networks with unbounded time varying delays[J]. IEEE Transactions on Neural Networks,2007,18(6): 1836-1840.