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)
Equilibrium and stability analysis of delayed neural networks under parameter uncertainties. (English) Zbl 1245.34075
A class of neural networks with multiple time delays under parameter uncertainties is studied. The authors prove existence, uniqueness and global asymptotic stability of an equilibrium of such net. In order to do this Lyapunov stability theorem and homeomophism mapping theorem are applied. In this way, delay-independent stability criteria are obtained in terms of network parameters. Numerical examples are provided as well.
MSC:
34K20Stability theory of functional-differential equations
92B20General theory of neural networks (mathematical biology)
34K21Stationary solutions of functional-differential equations
References:
[1]Ensari, T.; Arik, S.: New results for robust stability of dynamical neural networks with discrete time delays, Expert systems with applications 27, 5925-5930 (2010)
[2]Ozcan, N.; Arik, S.: An analysis of global robust stability of neural networks with discrete time delays, Physics letters A 359, 445-450 (2006) · Zbl 1193.92004 · doi:10.1016/j.physleta.2006.06.055
[3]Ozcan, N.; Arik, S.: Global robust stability analysis of neural networks with multiple time delays, IEEE transactions on circuits and systems I 53, 166-176 (2006)
[4]Liao, X. F.; Yu, J.: Robust stability for interval Hopfield neural networks with time delay, IEEE transactions on neural networks 9, 1042-1045 (1998)
[5]Sun, C.; Feng, C. B.: Global robust exponential stability of interval neural networks with delays, Neural processing letters 17, 107-115 (2003)
[6]Liao, X. F.; Wong, K. W.; Wu, Z.; Chen, G.: Novel robust stability for interval-delayed Hopfield neural, IEEE transactions on circuits and systems I 48, 1355-1359 (2001) · Zbl 1006.34071 · doi:10.1109/81.964428
[7]Chen, A.; Cao, J.; Huang, L.: Global robust stability of interval cellular neural networks with time-varying delays, Chaos, solitons and fractals 23, 787-799 (2005) · Zbl 1101.68752 · doi:10.1016/j.chaos.2004.05.029
[8]Cao, J.; Chen, T.: Global exponentially robust stability and periodicity of delayed neural networks, Chaos, solitons and fractals 22, 957-963 (2004) · Zbl 1061.94552 · doi:10.1016/j.chaos.2004.03.019
[9]Shao, J. L.; Huang, T. Z.; Wang, X. P.: Improved global robust exponential stability criteria for interval neural networks with time-varying delays, Expert systems with applications 38, 15587-15593 (2011)
[10]Han, W.; Kao, Y.; Wang, L.: Global exponential robust stability of static interval neural networks with S-type distributed delays, Journal of the franklin institute 348, 2072-2081 (2011)
[11]Deng, F.; Hua, M.; Liu, X.; Peng, Y.; Fei, J.: Robust delay-dependent exponential stability for uncertain stochastic neural networks with mixed delays, Neurocomputing 74, 1503-1509 (2011)
[12]Huang, T.: Robust stability of delayed fuzzy cohengrossberg neural networks, Computers and mathematics with applications 61, 2247-2250 (2011) · Zbl 1219.93094 · doi:10.1016/j.camwa.2010.09.037
[13]Mahmoud, M. S.; Ismail, A.: Improved results on robust exponential stability criteria for neutral-type delayed neural networks, Applied mathematics and computation 217, 3011-3019 (2010) · Zbl 1213.34084 · doi:10.1016/j.amc.2010.08.034
[14]Wang, Z.; Liu, Y.; Liu, X.; Shi, Yong: Robust state estimation for discrete-time stochastic neural networks with probabilistic measurement delays, Neurocomputing 74, 256-264 (2010)
[15]Balasubramaniam, P.; Ali, M. S.: Robust stability of uncertain fuzzy cellular neural networks with time-varying delays and reaction diffusion terms, Neurocomputing 74, 439-446 (2010)
[16]Singh, V.: New LMI-based criteria for global robust stability of delayed neural networks, Applied mathematical modelling 34, 2958-2965 (2010) · Zbl 1201.93099 · doi:10.1016/j.apm.2010.01.005
[17]Li, X.: Global robust stability for stochastic interval neural networks with continuously distributed delays of neutral type, Applied mathematics and computation 215, 4370-4384 (2010) · Zbl 1196.34107 · doi:10.1016/j.amc.2009.12.068
[18]Singh, V.: Modified criteria for global robust stability of interval delayed neural networks, Applied mathematics and computation 215, No. 15, 3124-3133 (2009) · Zbl 1189.34147 · doi:10.1016/j.amc.2009.10.006
[19]Guo, Z.; Huang, L.: LMI conditions for global robust stability of delayed neural networks with discontinuous neuron activations, Applied mathematics and computation 215, 889-900 (2009) · Zbl 1187.34098 · doi:10.1016/j.amc.2009.06.013
[20]Liu, L.; Han, Z.; Li, W.: Global stability analysis of interval neural networks with discrete and distributed delays of neutral type, Expert systems with applications 36, 7328-7331 (2009)
[21]Luo, M.; Zhong, S.; Wang, R.; Kang, Wei: Robust stability analysis for discrete-time stochastic neural networks systems with time-varying delays, Applied mathematics and computation 209, 305-313 (2009) · Zbl 1157.93027 · doi:10.1016/j.amc.2008.12.084
[22]Gao, M.; Cui, Baotong: Global robust exponential stability of discrete-time interval BAM neural networks with time-varying delays, Applied mathematical modelling 33, 1270-1284 (2009) · Zbl 1168.39300 · doi:10.1016/j.apm.2008.01.019
[23]Huang, Z.; Li, X.; Mohamad, S.; Lu, Z.: Robust stability analysis of static neural network with S-type distributed delays, Applied mathematical modelling 33, 760-769 (2009) · Zbl 1168.34353 · doi:10.1016/j.apm.2007.12.006
[24]Kwon, O. M.; Park, J. H.: New delay-dependent robust stability criterion for uncertain neural networks with time-varying delays, Applied mathematics and computation 205, 417-427 (2008) · Zbl 1162.34060 · doi:10.1016/j.amc.2008.08.020
[25]Park, J. H.; Kwon, O. M.: On improved delay-dependent criterion for global stability of bidirectional associative memory neural networks with time-varying delays, Applied mathematics and computation 199, 435-446 (2008) · Zbl 1149.34049 · doi:10.1016/j.amc.2007.10.001
[26]Li, H.; Chen, B.; Zhou, Q.; Fang, Shengle: Robust exponential stability for uncertain stochastic neural networks with discrete and distributed time-varying delays, Physics letters A 372, 3385-3394 (2008) · Zbl 1220.82085 · doi:10.1016/j.physleta.2008.01.060
[27]Shengyuan, X.; Lam, J.; Ho, D. W. C.; Zou, Y.: Improved global robust asymptotic stability criteria for delayed cellular neural networks, IEEE transactions on systems, man, and cybernetics, part B: cybernetics 35, 1317-1321 (2005)
[28]Marco, M. D.; Grazzini, M.; Pancioni, L.: Global robust stability criteria for interval delayed full-range cellular neural networks, IEEE transactions on neural networks 22, 666-671 (2011)
[29]Zhang, H.; Wang, Z.; Liu, D.: Robust stability analysis for interval cohengrossberg neural networks with unknown time-varying delays, IEEE transactions on neural networks 19, 1942-1955 (2008)
[30]Qi, H.: New sufficient conditions for global robust stability of delayed neural networks, IEEE transactions on circuits and systems I: Regular papers 54, 1131-1141 (2007)
[31]Shen, T.; Zhang, Y.: Improved global robust stability criteria for delayed neural networks, IEEE transactions on circuits and systems II: Express briefs 54, 715-719 (2007)
[32]Lee, S. M.; Kwon, O. M.; Park, J. H.: A new approach to stability analysis of neural networks with time-varying delay via novel Lyapunov – Krasovskiĭ function, Chinese physics B 19, 050507 (2010)
[33]Ji, D. H.; Koo, J. H.; Won, S. C.; Lee, S. M.; Park, Ju H.: Passivity-based control for Hopfield neural networks using convex representation, Applied mathematics and computation 217, 6168-6175 (2011) · Zbl 1209.93056 · doi:10.1016/j.amc.2010.12.100
[34]Lee, S. M.; Kwon, O. M.; Park, Ju H.: A novel delay-dependent criterion for delayed neural networks of neutral type, Physics letters A 374, 1843-1848 (2010)
[35]Zhang, H.; Liu, Z.; Huang, G. B.: Novel delay-dependent robust stability analysis for switched neutral-type neural networks with time-varying delays via SC technique, IEEE transactions on systems, man, and cybernetics, part B: cybernetics 40, 1480-1491 (2010)
[36]Cui, S.; Zhao, T.; Guo, J.: Global robust exponential stability for interval neural networks with delay, Chaos, solitons and fractals 42, 1567-1576 (2009) · Zbl 1198.93156 · doi:10.1016/j.chaos.2009.03.034
[37]Horn, R. A.; Johnson, C. R.: Topics in matrix analysis, (1991)