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)
Asymptotic stability of stochastic delayed recurrent neural networks with impulsive effects. (English) Zbl 1211.93108
Summary: In this paper, the asymptotic stability for a class of stochastic neural networks with time-varying delays and impulsive effects is considered. By employing the Lyapunov functional method combined with the linear matrix inequality optimization approach, a new set of sufficient conditions is derived for the asymptotic stability of stochastic delayed recurrent neural networks with impulses. A numerical example is given to show that the presented result significantly improves the allowable upper bounds of delays over some existing results in the literature.
MSC:
93D20Asymptotic stability of control systems
93B20Minimal systems representations
93D30Scalar and vector Lyapunov functions
60H10Stochastic ordinary differential equations
References:
[1]Cao, J., Wang, J.: Global asymptotic stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans. Circuits Syst. I 50, 34–44 (2003) · doi:10.1109/TCSI.2002.807494
[2]Chen, W., Lu, X.: Mean square exponential stability of uncertain stochastic delayed neural networks. Phys. Lett. A 372, 1061–1069 (2008) · Zbl 1217.92005 · doi:10.1016/j.physleta.2007.09.009
[3]Chen, B., Wang, J.: Global exponential periodicity and global exponential stability of a class of recurrent neural networks. Phys. Lett. A 329, 36–48 (2004) · Zbl 1208.81063 · doi:10.1016/j.physleta.2004.06.072
[4]Chen, B., Wang, J.: Global exponential periodicity and global exponential stability of a class of recurrent neural networks with various activation functions and time-varying delays. Neural Netw. 20, 1067–1080 (2007) · Zbl 1254.34114 · doi:10.1016/j.neunet.2007.07.007
[5]Chen, W., Guan, Z., Liu, X.: Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: an LMI approach. Syst. Control Lett. 54, 547–555 (2005) · Zbl 1129.93547 · doi:10.1016/j.sysconle.2004.10.005
[6]Cichocki, A., Unbehauen, R.: Neural Networks for Optimization and Signal Processing. Wiley, Chichester (1993)
[7]Dong, M., Zhang, H., Wang, Y.: Dynamics analysis of impulsive stochastic Cohen-Grossberg neural networks with Markovian jumping and mixed time delays. Neurocomputing 72, 1999–2004 (2009) · Zbl 05719002 · doi:10.1016/j.neucom.2008.12.007
[8]Gu, K.Q., Kharitonov, V.L., Chen, J.: Stability of Time-Delay Systems. Birkhäuser, Boston (2003)
[9]Haykin, S.: Neural Networks. Prentice-Hall, Englewood Cliffs (1994)
[10]Hien, L.V., Ha, Q.P., Phat, V.N.: Stability and stabilization of switched linear dynamic systems with time delay and uncertainties. Appl. Math. Comput. 210, 223–231 (2009) · Zbl 1159.93351 · doi:10.1016/j.amc.2008.12.082
[11]Huang, H., Feng, G.: Delay-dependent stability analysis for uncertain stochastic neural networks with time-varying delay. Physica A 381, 93–103 (2007) · doi:10.1016/j.physa.2007.04.020
[12]Kwon, O.M., Park, J.H.: Improved delay-dependent stability criterion for neural networks with time-varying delays. Phys. Lett. A 373, 529–535 (2009) · Zbl 1227.34030 · doi:10.1016/j.physleta.2008.12.005
[13]Kwon, O.M., Park, J.H., Lee, S.M.: On robust stability for uncertain neural networks with interval time-varying delays. IET Control. Theory Appl. 7, 625–634 (2008) · doi:10.1049/iet-cta:20070325
[14]Li, H., Chen, B., Zhou, Q., Fang, S.: Robust exponential stability for uncertain stochastic neural networks with discrete and distributed time-varying delays. Phys. Lett. A 372, 3385–3394 (2008) · Zbl 1220.82085 · doi:10.1016/j.physleta.2008.01.060
[15]Liang, J., Wang, Z., Liu, X.: State estimation for coupled uncertain stochastic networks with missing measurements and time-varying delays: the discrete-time case. IEEE Trans. Neural Netw. 20, 781–793 (2009) · doi:10.1109/TNN.2009.2013240
[16]Liu, Y.R., Wang, Z.D., Liu, X.H.: On global exponential stability of generalized stochastic neural networks with mixed time-delays. Neurocomputing 70, 314–326 (2006) · Zbl 05184833 · doi:10.1016/j.neucom.2006.01.031
[17]Liu, Y., Wang, Z., Liang, J., Liu, X.: Stability and synchronization of discrete-time Markovian jumping neural networks with mixed model-dependent time-delays. IEEE Trans. Neural Netw. 20, 1102–1116 (2009) · doi:10.1109/TNN.2009.2016210
[18]Phat, V.N., Ha, Q.P.: H control and exponential stability of nonlinear nonautonomous systems with time-varying delay. J. Optim. Theory Appl. 142, 603–618 (2009) · Zbl 1178.93047 · doi:10.1007/s10957-009-9512-9
[19]Rakkiyappan, R., Balasubramaniam, P.: LMI conditions for stability of stochastic recurrent neural networks with distributed delays. Chaos Solitons Fractals 40, 1688–1696 (2009) · Zbl 1198.34161 · doi:10.1016/j.chaos.2007.09.052
[20]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 372, 5290–5298 (2008) · Zbl 1223.92001 · doi:10.1016/j.physleta.2008.06.011
[21]Wan, L., Sun, J.: Mean square exponential stability of stochastic delayed Hopfield neural networks. Phys. Lett. A 343, 306–318 (2005) · Zbl 1194.37186 · doi:10.1016/j.physleta.2005.06.024
[22]Wang, Z.D., Liu, Y.R., Fraser, K., Liu, X.H.: Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays. Phys. Lett. A 354, 288–297 (2006) · Zbl 1181.93068 · doi:10.1016/j.physleta.2006.01.061
[23]Wang, Z.D., Liu, Y.Y., Li, M., Liu, X.H.: Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Trans. Neural Netw. 17, 814–820 (2006) · doi:10.1109/TNN.2006.872355
[24]Wang, Y., Wang, Z., Liang, J.: A delay fractioning approach to global synchronization of delayed complex networks with stochastic disturbances. Phys. Lett. A 372, 6066–6073 (2008) · Zbl 1223.90013 · doi:10.1016/j.physleta.2008.08.008
[25]Zhu, W.L., Hu, J.: Stability analysis of stochastic delayed cellular neural networks by LMI approach. Chaos Solitons Fractals 29, 171–174 (2006) · Zbl 1095.92003 · doi:10.1016/j.chaos.2005.08.049