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)
Mixed time-delays dependent exponential stability for uncertain stochastic high-order neural networks. (English) Zbl 1206.65025
Authors’ abstract: This paper presents a discrete and distributed time-delays dependent simultaneous approach to deterministic and uncertain stochastic high-order neural networks. New results are proposed in terms of a linear matrix inequality by exploiting a novel Lyapunov-Krasovskii functional and by making use of novel techniques for time-delay systems. Some constraints on the systems are removed, and the new results cover some recently published works. Two numerical examples are given to show the usefulness of presented approach.
MSC:
65C30Stochastic differential and integral equations
60H10Stochastic ordinary differential equations
60H35Computational methods for stochastic equations
65L20Stability and convergence of numerical methods for ODE
References:
[1]Dembo, A.; Farotimi, O.; Kailath, T.: High-order absolutely stable neural networks, IEEE trans. Circ. syst. 38, 57-65 (1991) · Zbl 0712.92002 · doi:10.1109/31.101303
[2]Psaltis, D.; Park, C. H.; Hong, J.: Higher order associative memories and their optical implementations, Neural networks 1, 143-163 (1988)
[3]Karayiannis, N. B.; Venetsanopoulos, A. N.: On the training and performance of high-order neural networks, Math. biosci. 129, 143-168 (1995) · Zbl 0830.92005 · doi:10.1016/0025-5564(94)00057-7
[4]Artyomov, E.; Yadid-Pecht, O.: Modified high-order neural network for invariant pattern recognition, Pattern recognit. Lett. 26, 843-851 (2005)
[5]He, Y.; Wang, Q. -G.; Xie, L.; Lin, C.: Further improvement of free-weighting matrices technique for systems with time-varying delay, IEEE trans. Autom. control 52, 293-299 (2007)
[6]Ma, S.; Zhang, C.; Wu, Z.: Delay-dependent stability and H control for uncertain discrete switched singular systems with time-delay, Appl. math. Comput. 206, 413-424 (2008) · Zbl 1152.93461 · doi:10.1016/j.amc.2008.09.020
[7]Rakkiyappan, R.; Balasubramaniam, P.: LMI conditions for global asymptotic stability results for neutral-type neural networks with distributed time delays, Appl. math. Comput. 204, 317-324 (2008) · Zbl 1168.34356 · doi:10.1016/j.amc.2008.06.049
[8]Ibrir, S.: Stability and robust stabilization of discrete-time switched systems with time-delays: LMI approach, Appl. math. Comput. 206, 570-578 (2008) · Zbl 1152.93493 · doi:10.1016/j.amc.2008.05.149
[9]Xie, L.: Output feedback H control of systems with parameter uncertainty, Int. J. Control 63, 741-750 (1996) · Zbl 0841.93014 · doi:10.1080/00207179608921866
[10]Cao, J.; Liang, J.; Lam, J.: Exponential stability of high-order bidirectional associative memory neural networks with time delays, Physica D: Nonlinear phenom. 199, 425-436 (2004) · Zbl 1071.93048 · doi:10.1016/j.physd.2004.09.012
[11]Ren, F.; Cao, J.: LMI-based criteria for stability of high-order neural networks with time-varying delay, Nonlinear anal. Ser. B: real world appl. 7, 967-979 (2006) · Zbl 1121.34078 · doi:10.1016/j.nonrwa.2005.09.001
[12]Wang, Z.; Fang, J.; Liu, X.: Global stability of stochastic high-order neural networks with discrete and distributed delays, Chaos, solitons & fractals 36, 388-396 (2008) · Zbl 1141.93416 · doi:10.1016/j.chaos.2006.06.063
[13]Blythe, S.; Mao, X.; Liao, X.: Stability of stochastic delay neural networks, J. franklin inst. 338, 481-495 (2001) · Zbl 0991.93120 · doi:10.1016/S0016-0032(01)00016-3
[14]Huang, H.; Ho, D. W. C.; Lam, J.: Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays, IEEE trans. Circ. syst.: part II 52, 251-255 (2005)
[15]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
[16]Ruan, S.; Filfil, R. S.: Dynamics of a two-neuron system with discrete and distributed delays, Physica D 191, 323-342 (2004) · Zbl 1049.92004 · doi:10.1016/j.physd.2003.12.004
[17]Zhao, H.: Global asymptotic stability of Hopfield neural network involving distributed delays, Neural networks 17, 47-53 (2004) · Zbl 1082.68100 · doi:10.1016/S0893-6080(03)00077-7
[18]Zhao, H.: Existence and global attractivity of almost periodic solution for cellular neural network with distributed delays, Appl. math. Comput. 154, 683-695 (2004) · Zbl 1057.34099 · doi:10.1016/S0096-3003(03)00743-4
[19]Tang, Y.; Qiu, R.; Fang, J.; Miao, Q.; Xia, M.: Adaptive lag synchronization in unknown stochastic chaotic neural networks with discrete and distributed time-varying delays, Phys. lett. A 372, 4425-4433 (2008) · Zbl 1221.82078 · doi:10.1016/j.physleta.2008.04.032
[20]Wang, Z.; Liu, Y.; Liu, X.: On global asymptotic stability of neural networks with discrete and distributed delays, Phys. lett. A 345, 299-308 (2005)
[21]Wang, Z.; Shu, H.; Liu, Y.; Ho, D. W. C.; Liu, X.: Robust stability analysis of generalized neural networks with discrete and distributed time delays, Chaos, solitons & fractals 30, 886-896 (2006) · Zbl 1142.93401 · doi:10.1016/j.chaos.2005.08.166
[22]Wang, Z.; Lauria, S.; Fang, J.; Liu, X.: Exponential stability of uncertain stochastic neural networks with mixed time-delays, Chaos, solitons & fractals 32, 62-72 (2007)
[23]Tang, Y.; Wang, Z.; Fang, J.: Pinning control of fractional-order weighted complex networks, Chaos 19, 013112 (2009)
[24]Hale, J. K.: Theory of functional differential equations, (1977)
[25]Boyd, S.; Ghaoui, L. E.; Feron, E.; Balakrishnan, V.: Linear matrix inequalities in system and control theory, (1994)
[26]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, 2000, pp. 2805 – 2810.
[27]Petersen, I. R.: A stabilization algorithm for a class of uncertain linear systems, Syst. control lett. 8, 351-357 (1987) · Zbl 0618.93056 · doi:10.1016/0167-6911(87)90102-2
[28]Friedman, A.: Stochastic differential equations and their applications, (1976)