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)
Improved stability analysis on delayed neural networks with linear fractional uncertainties. (English) Zbl 1209.34087
Summary: The paper is concerned with the robust stability for generalized neural networks with both interval time-varying delay and time-varying distributed delay. Through partitioning the time-delay, choosing an augmented Lyapunov-Krasovskii functional, employing the free-weighting matrix method and convex combination, sufficient conditions are obtained to guarantee the robust stability of the concerned systems.
MSC:
34K20Stability theory of functional-differential equations
92B20General theory of neural networks (mathematical biology)
34K37Functional-differential equations with fractional derivatives
References:
[1]Song, Q.; Cao, J.: Robust stability in Cohen – Grossberg neural network with doth time-varying and distributed delays, Neural process lett. 27, 179-196 (2008)
[2]Senan, S.; Arik, S.: Global robust stability of bidirectional associative memory neural networks with multiple time delays, IEEE trans. Syst. man cybern. B 37, 1375-1381 (2007)
[3]Zhang, X.; Han, Q.: New Lyapunov – Krasovskiĭ functionals for global asymptotic stability of delayed neural networks, IEEE trans. Neural networks 20, 533-539 (2009)
[4]Syed, M.; Balasubramaniam, A. P.: Stability analysis of uncertain fuzzy Hopfield neural networks with time delays, Commun. nonlinear sci. Numer. simul. 14, 2776-2783 (2009) · Zbl 1221.34191 · doi:10.1016/j.cnsns.2008.09.024
[5]Song, K.; Cao, J.: Impulsive effects on stability of fuzzy Cohen – Grossberg neural networks with time-varying delays, IEEE trans. Syst. man cybern. Part B 37, 733-741 (2007)
[6]Liu, R.; Wang, Z.; Liu, X.: On global sability of delayed BAM stochastic neural networks with Markovian switching, Neural process lett. 30, 19-35 (2009)
[7]Yucel, E.; Arik, S.: Novel results for global robust stability of delayed neural networks, Chaos soliton. Fract. 39, 1604-1614 (2009) · Zbl 1197.34148 · doi:10.1016/j.chaos.2007.06.052
[8]Ozcan, N.; Arik, S.: A new sufficient condition for global robust stability of bidirectional associative memory neural networks with multiple time delays, Nonlinear anal: realworld appl. 10, 3312-3320 (2009) · Zbl 1162.92005 · doi:10.1016/j.nonrwa.2008.07.001
[9]Chen, W.; Zheng, W.: Improved delay-dependent asymptotical stability criteria for delayed neural networks, IEEE trans. Neural networks-II 19, 2154-2161 (2008)
[10]Wu, M.; Liu, F.; Shi, P.: Exponential stability analysis for neural networks with time-varying delay, IEEE trans. Syst. man cybern. Part B 38, 1152-1156 (2008)
[11]Singh, V.: Improved global robust stability for interval-delayed Hopfield neural networks, Neural process lett. 27, 257-265 (2008)
[12]Yang, R.; Gao, H.; Shi, P.: Novel robust stability criteria for stochastic Hopfield neural networks with time delays, IEEE trans. Syst. man cybern. Part B 39, 467-474 (2009)
[13]Mou, S.; Gao, H.; Qiang, W.: New delay-dependent exponential stability for neural networks with time delay, IEEE trans. Syst. man cybern. Part B, 571-576 (2008)
[14]Kwon, O. M.; Park, J. H.; Lee, S. M.: On robust stability for uncertain neural networks with interval time-varying delays, IET control theor. Appl. 2, 625-634 (2008)
[15]Kwon, O. M.; Park, J. H.: Exponential stability analysis for uncertain neural networks with interval time-varying delays, Appl. math. Comput. 212, 530-541 (2009) · Zbl 1179.34080 · doi:10.1016/j.amc.2009.02.043
[16]Hou, Y.; Liao, T.; Lien, C.; Yan, J.: Stability analysis of neural networks with interval time-varying delays, Chaos solition. Fract. 17, 103-120 (2007) · Zbl 1163.37334 · doi:10.1063/1.2771082
[17]He, Y.; Liu, G.; Rees, D.; Wu, M.: Stability analysis for neural networks with time-varying interval delay, IEEE trans. Neural networks 18, 1850-1854 (2007)
[18]Hu, L.; Gao, H.; Zheng, W.: Novel stability of cellular neural networks with interval time-varying delay, Neural networks 21, 1458-1463 (2008)
[19]Rakkiyappan, R.; Balasubramaniam, P.; Lakshmanan, S.: Robust stability results for uncertain stochastic neural networks with discrete interval and distributed time-varying delays, Phys. lett. A 273, 5290-5298 (2008) · Zbl 1223.92001 · doi:10.1016/j.physleta.2008.06.011
[20]Song, R.; Wang, Z.: Neural networks with discrete and distributed time-varying delays: A general stability analysis, Chaos soliton. Fract. 37, 1538-1547 (2008) · Zbl 1142.34380 · doi:10.1016/j.chaos.2006.10.044
[21]Rakkiyappan, R.; Balasubramaniam, P.: Delay-dependent robust stability analysis for Markovian jumping stochastic Cohen – Grossberg neural networks with discrete interval and distributed time-varying delays, Nonlinear anal: hybrid syst. 3, 207-214 (2009) · Zbl 1184.93093 · doi:10.1016/j.nahs.2009.01.002
[22]Rakkiyappan, R.; Balasubramaniam, P.: Delay-dependent robust stability analysis of uncertain stochastic neural networks with discrete interval and distributed time-varying delays, Neurocomputing 72, 3231-3237 (2009)
[23]Gao, M.; Cui, B.: Global robust stability of neural networks with multiple discrete delays and distributed delays, Chaos soliton. Fract. 40, 1823-1834 (2009) · Zbl 1198.93159 · doi:10.1016/j.chaos.2007.09.065
[24]Wang, Z.; H., H. Shu; Liu, R.: Robust stability analysis of generalized neural networks with discrete and distributed time delays, Chaos soliton. Fract. 30, 886-896 (2006) · Zbl 1142.93401 · doi:10.1016/j.chaos.2005.08.166
[25]Wang, Z.; Liu, D.; Zhang, H.: Global asymptotic stability and robust stability of a class of Cohen – Grossberg neural networks with mixed delays, IEEE trans. Circ. syst-I. 56, 616-629 (2009)
[26]Li, T.; Fei, S.: Stability analysis of Cohen – Grossberg neural networks with time-varying and distributed delays, Neurocomputing 71, 1069-1081 (2008)
[27]Wang, Z.; Zhang, H.; Yu, W.: Robust stability of Cohen – Grossberg neural networks via state transmission matrix, IEEE trans. Neural networks. 20, 169-174 (2009)
[28]Yue, D.; Tian, E.; Zhang, Y.; Peng, C.: Delay-distribution-dependent stability and stabilization of T-S fuzzy systems with probabilistic interval delay, IEEE trans. Syst. man cybern. Part B 39, 503-516 (2009)
[29]Long, F.; Fei, S.; Fu, Z.: H control and quadratic stabilization of switched linear systems with linear fractional uncertainties via output feedback, Nonlinear anal: hybrid syst. 2, 18-27 (2008) · Zbl 1157.93365 · doi:10.1016/j.nahs.2006.11.004
[30]Guo, Z.; Huang, L.: LMI conditions for global robust stability of delayed neural networks with discontinuous neuron activations, Appl. math. Comput. 215, 889-900 (2009) · Zbl 1187.34098 · doi:10.1016/j.amc.2009.06.013
[31]Zhou, Q.; Wan, L.: Global robust asymptotic stability analysis of BAM neural networks with time delay and impulse: an LMI approach, Appl. math. Comput. 216, 1538-1545 (2010) · Zbl 1200.34088 · doi:10.1016/j.amc.2010.03.003
[32]Park, J. H.; Kwon, O. M.: Further results on state estimation for neural networks of neutral-type with time-varying delay, Appl. math. Comput. 208, 69-75 (2009) · Zbl 1169.34334 · doi:10.1016/j.amc.2008.11.017
[33]Park, J. H.; Kwon, O. M.: On improved delay-dependent criterion for global stability of bidirectional associative memory neural networks with time-varying delays, Appl. math. Comput. 199, 435-446 (2008) · Zbl 1149.34049 · doi:10.1016/j.amc.2007.10.001