zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Global robust exponential stability analysis for interval neural networks with mixed delays. (English) Zbl 1256.93079
Summary: A class of interval neural networks with time-varying delays and distributed delays is investigated. By employing $H$-matrix and $M$-matrix theory, homeomorphism techniques, the Lyapunov functional method, and the linear matrix inequality approach, sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point to the neural networks are established and some previously published results are improved and generalized. Finally, some numerical examples are given to illustrate the effectiveness of the theoretical results.
MSC:
93D09Robust stability of control systems
34K35Functional-differential equations connected with control problems
34K20Stability theory of functional-differential equations
WorldCat.org
Full Text: DOI
References:
[1] S. Arik, “Global robust stability analysis of neural networks with discrete time delays,” Chaos, Solitons and Fractals, vol. 26, no. 5, pp. 1407-1414, 2005. · Zbl 1122.93397 · doi:10.1016/j.chaos.2005.03.025
[2] T. Ensari and S. Arik, “New results for robust stability of dynamical neural networks with discrete time delays,” Expert Systems with Applications, vol. 37, no. 8, pp. 5925-5930, 2010. · doi:10.1016/j.eswa.2010.02.013
[3] O. Faydasicok and S. Arik, “Further analysis of global robust stability of neural networks with multiple time delays,” Journal of the Franklin Institute, vol. 349, no. 3, pp. 813-825, 2012. · Zbl 1273.93124 · doi:10.1016/j.jfranklin.2011.11.007
[4] O. Faydasicok and S. Arik, “A new robust stability criterion for dynamical neural networks with multiple time delays,” Neurocomputing, vol. 99, no. 1, pp. 290-297, 2013. · Zbl 1296.92085
[5] W. Han, Y. Liu, and L. Wang, “Robust exponential stability of Markovian jumping neural networks with mode-dependent delay,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 9, pp. 2529-2535, 2010. · Zbl 1222.93231 · doi:10.1016/j.cnsns.2009.09.024
[6] N. Ozcan and S. Arik, “Global robust stability analysis of neural networks with multiple time delays,” IEEE Transactions on Circuits and Systems I, vol. 53, no. 1, pp. 166-176, 2006. · Zbl 1193.92004 · doi:10.1109/TCSI.2005.855724
[7] V. Singh, “Improved global robust stability criterion for delayed neural networks,” Chaos, Solitons and Fractals, vol. 31, no. 1, pp. 224-229, 2007. · Zbl 1142.93400 · doi:10.1016/j.chaos.2005.09.050
[8] W. Zhao and Q. Zhu, “New results of global robust exponential stability of neural networks with delays,” Nonlinear Analysis: Real World Applications, vol. 11, no. 2, pp. 1190-1197, 2010. · Zbl 1196.34098 · doi:10.1016/j.nonrwa.2009.01.008
[9] F. Wang and H. Wu, “Mean square exponential stability and periodic solutions of stochastic interval neural networks with mixed time delays,” Neurocomputing, vol. 73, no. 16-18, pp. 3256-3263, 2010. · doi:10.1016/j.neucom.2010.04.020
[10] P. Balasubramaniam and G. Nagamani, “A delay decomposition approach to delay-dependent passivity analysis for interval neural networks with time-varying delay,” Neurocomputing, vol. 74, no. 10, pp. 1646-1653, 2011. · doi:10.1016/j.neucom.2011.01.011
[11] P. Balasubramaniam, G. Nagamani, and R. Rakkiyappan, “Global passivity analysis of interval neural networks with discrete and distributed delays of neutral type,” Neural Processing Letters, vol. 32, no. 2, pp. 109-130, 2010. · doi:10.1007/s11063-010-9147-8
[12] P. Balasubramaniam and M. S. Ali, “Robust exponential stability of uncertain fuzzy Cohen-Grossberg neural networks with time-varying delays,” Fuzzy Sets and Systems, vol. 161, no. 4, pp. 608-618, 2010. · Zbl 1185.68511 · doi:10.1016/j.fss.2009.10.013
[13] O. M. Kwon, S. M. Lee, and J. H. Park, “Improved delay-dependent exponential stability for uncertain stochastic neural networks with time-varying delays,” Physics Letters A, vol. 374, no. 10, pp. 1232-1241, 2010. · Zbl 1236.92006 · doi:10.1016/j.physleta.2010.01.007
[14] S. Lakshmanan, A. Manivannan, and P. Balasubramaniam, “Delay-distribution-dependent stability criteria for neural networks with time-varying delays,” Dynamics of Continuous, Discrete and Impulsive Systems A, vol. 19, no. 1, pp. 1-14, 2012. · Zbl 1268.34166
[15] J. L. Shao, T. Z. Huang, and X. P. Wang, “Improved global robust exponential stability criteria for interval neural networks with time-varying delays,” Expert Systems with Applications, vol. 38, no. 12, pp. 15587-15593, 2011. · doi:10.1016/j.eswa.2011.05.066
[16] J. L. Shao, T. Z. Huang, and S. Zhou, “An analysis on global robust exponential stability of neural networks with time-varying delays,” Neurocomputing, vol. 72, no. 7-9, pp. 1993-1998, 2009. · doi:10.1016/j.neucom.2008.11.023
[17] J.-L. Shao, T.-Z. Huang, and S. Zhou, “Some improved criteria for global robust exponential stability of neural networks with time-varying delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 12, pp. 3782-3794, 2010. · Zbl 1222.93175 · doi:10.1016/j.cnsns.2010.02.002
[18] Z. Wang, H. Zhang, and W. Yu, “Robust stability criteria for interval Cohen-Grossberg neural networks with time varying delay,” Neurocomputing, vol. 72, no. 4-6, pp. 1105-1110, 2009. · doi:10.1016/j.neucom.2008.03.001
[19] H. Zhang, Z. Wang, and D. Liu, “Robust exponential stability of recurrent neural networks with multiple time-varying delays,” IEEE Transactions on Circuits and Systems II, vol. 54, no. 8, pp. 730-734, 2007. · doi:10.1109/TCSII.2007.896799
[20] J. Zhang, “Global exponential stability of interval neural networks with variable delays,” Applied Mathematics Letters, vol. 19, no. 11, pp. 1222-1227, 2006. · Zbl 1180.34083 · doi:10.1016/j.aml.2006.01.005
[21] X. Li, “Global robust stability for stochastic interval neural networks with continuously distributed delays of neutral type,” Applied Mathematics and Computation, vol. 215, no. 12, pp. 4370-4384, 2010. · Zbl 1196.34107 · doi:10.1016/j.amc.2009.12.068
[22] W. Su and Y. Chen, “Global robust stability criteria of stochastic Cohen-Grossberg neural networks with discrete and distributed time-varying delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 2, pp. 520-528, 2009. · Zbl 1221.37196 · doi:10.1016/j.cnsns.2007.09.001
[23] H. Liu, Y. Ou, J. Hu, and T. Liu, “Delay-dependent stability analysis for continuous-time BAM neural networks with Markovian jumping parameters,” Neural Networks, vol. 23, no. 3, pp. 315-321, 2010. · doi:10.1016/j.neunet.2009.12.001
[24] J. Pan, X. Liu, and S. Zhong, “Stability criteria for impulsive reaction-diffusion Cohen-Grossberg neural networks with time-varying delays,” Mathematical and Computer Modelling, vol. 51, no. 9-10, pp. 1037-1050, 2010. · Zbl 1198.35033 · doi:10.1016/j.mcm.2009.12.004
[25] J. Tian and S. Zhong, “Improved delay-dependent stability criterion for neural networks with time-varying delay,” Applied Mathematics and Computation, vol. 217, no. 24, pp. 10278-10288, 2011. · Zbl 1225.34080 · doi:10.1016/j.amc.2011.05.029
[26] H. Wang, Q. Song, and C. Duan, “LMI criteria on exponential stability of BAM neural networks with both time-varying delays and general activation functions,” Mathematics and Computers in Simulation, vol. 81, no. 4, pp. 837-850, 2010. · Zbl 1204.92006 · doi:10.1016/j.matcom.2010.08.011
[27] X. Zhang, S. Wu, and K. Li, “Delay-dependent exponential stability for impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 3, pp. 1524-1532, 2011. · Zbl 1221.35440 · doi:10.1016/j.cnsns.2010.06.023
[28] K. Li, “Stability analysis for impulsive Cohen-Grossberg neural networks with time-varying delays and distributed delays,” Nonlinear Analysis: Real World Applications, vol. 10, no. 5, pp. 2784-2798, 2009. · Zbl 1162.92002 · doi:10.1016/j.nonrwa.2008.08.005
[29] X. Fu and X. Li, “LMI conditions for stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 1, pp. 435-454, 2011. · Zbl 1221.34195 · doi:10.1016/j.cnsns.2010.03.003
[30] B. Zhou, Q. Song, and H. Wang, “Global exponential stability of neural networks with discrete and distributed delays and general activation functions on time scales,” Neurocomputing, vol. 74, no. 17, pp. 3142-3150, 2011. · doi:10.1016/j.neucom.2011.04.008
[31] R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, UK, 1991. · Zbl 0729.15001 · doi:10.1017/CBO9780511840371
[32] J. C. Principe, J. M. Kuo, and S. Celebi, “An analysis of the gamma memory in dynamic neural networks,” IEEE Transactions on Neural Networks, vol. 5, no. 2, pp. 331-337, 1994. · doi:10.1109/72.279195