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)
Exponential stability analysis for uncertain neural networks with interval time-varying delays. (English) Zbl 1179.34080
The authors establish exponential stability for neural networks with norm-bounded parametric uncertainties and interval time-varying delays. New delay-dependent exponential stability criteria with an exponential convergence rate are presented by means of linear matrix inequalities and Lyapunov method. Two numerical examples are considered.
MSC:
34K20Stability theory of functional-differential equations
92B20General theory of neural networks (mathematical biology)
34K25Asymptotic theory of functional-differential equations
References:
[1]Haykin, S.: Neural networks – A comprehensive foundation, (1998)
[2]Sun, Y.; Cao, J.: Pth moment exponential stability of stochastic Cohen – Grossberg neural networks with time-varying delays, Nonlinear analysis – real world applications 8, 1171-1185 (2007) · Zbl 1196.60125 · doi:10.1016/j.nonrwa.2006.06.009
[3]Cao, J.: Global asymptotic stability of neural networks with transmission delays, International journal of system sciences 31, 1313-1316 (2000) · Zbl 1080.93517 · doi:10.1080/00207720050165807
[4]Arik, S.: Global asymptotic stability of a larger class of neural networks with constant time delay, Physics letters A 311, 504-511 (2003) · Zbl 1098.92501 · doi:10.1016/S0375-9601(03)00569-3
[5]Cao, J.; Ho, D. W. C.; Huang, X.: LMI-based criteria for global robust stability of bidirectional associative memory networks with time delay, Nonlinear analysis 66, 1558-1572 (2007) · Zbl 1120.34055 · doi:10.1016/j.na.2006.02.009
[6]Ensari, T.; Arik, S.: Global stability of class of neural networks with time varying delays, IEEE transactions on circuits systems II – regular papers 52, 126-130 (2005)
[7]Ensari, T.; Arik, S.: Global stability analysis of neural networks with multiple time varying delays, IEEE transactions on automatic control 50, 1781-1785 (2005)
[8]Hua, C. C.; Long, C. N.; Guan, X. P.: New results on stability analysis of neural networks with time-varying delays, Physics letters A 352, 335-340 (2006) · Zbl 1187.34099 · doi:10.1016/j.physleta.2005.12.005
[9]Park, J. H.: A new stability analysis of delayed cellular neural networks, Applied mathematics and computations 181, 200-206 (2006) · Zbl 1154.34386 · doi:10.1016/j.amc.2006.01.024
[10]Zhang, Q.; Wei, X.; Xu, J.: Delay-dependent exponential stability of cellular neural networks with time-varying delays, Chaos, solitons & fractals 23, 1363-1369 (2005)
[11]Kwon, O. M.; Park, J. H.; Lee, S. M.: On robust stability for uncertain neural networks with interval time-varying delays, IET control theory and applications 7, 625-634 (2008)
[12]J.H. Park, O.M. Kwon, Global stability for neural networks of neutral-type with interval time-varying delays, Chaos, Solitons amp; Fractals, doi:10.1016/j.chaos.2008.04.049. · Zbl 1198.34158 · doi:10.1016/j.chaos.2008.04.049
[13]Gau, R. S.; Lien, C. H.; Hsieh, J. G.: Global exponential stability of uncertain cellular neural networks with multiple time-varying delays via LMI approach, Chaos, solitons & fractals 32, 1258-1267 (2007) · Zbl 1134.34049 · doi:10.1016/j.chaos.2005.11.036
[14]Kwon, O. M.; Park, J. H.: Exponential stability for uncertain cellular neural networks with discrete and distributed time-varying delays, Applied mathematics and computations 203, 813-823 (2008) · Zbl 1170.34052 · doi:10.1016/j.amc.2008.05.091
[15]Mou, S.; Gao, H.; Qiang, W.; Chen, K.: New delay-dependent exponential stability for neural networks with time delay, IEEE transactions on systems, man, and cybernetics B 38, 571-576 (2008)
[16]Park, J. H.: Further note on global exponential stability of uncertain cellular neural networks with variable delays, Applied mathematics and computations 188, 850-854 (2007) · Zbl 1126.34376 · doi:10.1016/j.amc.2006.10.036
[17]Zhang, B.; Xu, S.; Li, Y.: Delay-dependent robust exponential stability for uncertain recurrent neural networks with time-varying delays, International journal of neural systems 17, 207-218 (2007)
[18]Boyd, S.; Ghaoui, L. El.; Feron, E.; Balakrishnan, V.: Linear matrix inequalities in system and control theory, (1994)
[19]K. Gu, An integral inequality in the stability problem of time-delay systems, in: Proceedings of 39th IEEE Conference on Decision and Control, Sydney, Australia, December, 2000, pp. 2805 – 2810.