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)
Global robust exponential stability of discrete-time interval BAM neural networks with time-varying delays. (English) Zbl 1168.39300
Summary: This paper is concerned with global robust exponential stability for a class of discrete-time interval bidirectional associative memory (BAM) neural networks with time-varying delays. By employing the Lyapunov functional and linear matrix inequality (LMI) approach, a new sufficient criterion is proposed for the global robust exponential stability of discrete-time BAM neural networks which contain uncertain parameters with their values being bounded. The proposed LMI-based results are computationally efficient as they can be easily checked via the LMI toolbox. Finally, two examples are provided to demonstrate the effectiveness of the obtained results.
MSC:
 39A11 Stability of difference equations (MSC2000) 92B20 General theory of neural networks (mathematical biology)
References:
 [1] Kosko, B.: Neural networks and fuzzy systems-A dynamical system approach to machine intelligence, (1992) · Zbl 0755.94024 [2] Kosko, B.: Adaptive bi-directional associative memories, Appl. opt. 26, No. 23, 4947-4960 (1987) [3] Kosko, B.: Bi-directional associative memories, IEEE trans. Syst. man cybernet. 18, No. 1, 49-60 (1988) [4] Arik, S.: Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays, IEEE trans. Neural netw. 16, No. 3, 580-586 (2005) [5] Liao, X.; Wong, K. W.: Robust stability of interval bidirectional associative memory neural network with time delays, IEEE trans. Syst. man cybern. 34, No. 2, 1142-1154 (2004) [6] Lou, X.; Cui, B.: On the global robust asymptotic stability of BAM neural networks with time-varying delays, Neurocomputing 70, 273-279 (2006) [7] Lou, X.; Cui, B.: Global asymptotic stability of delay BAM neural networks with impulses based on matrix theory, Appl. math. Modell. 32, 232-239 (2008) · Zbl 1141.93399 · doi:10.1016/j.apm.2006.11.015 [8] Liu, Z.; Chen, A.; Cao, J.; Huang, L.: Existence and global exponential stability of periodic solution for BAM neural networks with periodic coefficients and time-varying delays, IEEE trans. Circ. syst. I 50, No. 9, 1162-1173 (2003) [9] Cui, B.; Lou, X.: Global asymptotic stability of BAM neural networks with distributed delays and reaction – diffusion terms, Chaos solitons fract. 27, 1347-1354 (2006) [10] Mohamad, S.: Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks, Physica D 159, 233-251 (2001) · Zbl 0984.92502 · doi:10.1016/S0167-2789(01)00344-X [11] Liang, J.; Cao, J.: Exponential stability of continuous-time and discrete-time bidirectional associative memory networks with delays, Chaos, solitons fract. 22, 773-785 (2004) · Zbl 1062.68102 · doi:10.1016/j.chaos.2004.03.004 [12] Liu, X.; Tang, M.; Martin, R.; Liu, X.: Discrete-time BAM neural networks with variable delays, Phys. lett. A 367, 322-330 (2007) · Zbl 1209.93112 · doi:10.1016/j.physleta.2007.03.037 [13] Cao, J.; Dong, M.: Exponential stability of delayed bidirectional associative memory networks, Appl. math. Comput. 135, 105-112 (2003) · Zbl 1030.34073 · doi:10.1016/S0096-3003(01)00315-0 [14] Li, Y.: Global exponential stability of BAM neural networks with delays and impulses, Chaos, solitons fract. 24, 279-285 (2005) · Zbl 1099.68085 · doi:10.1016/j.chaos.2004.09.027 [15] Lou, X.; Cui, B.: Stochastic exponential stability for Markovian jumping BAM neural networks with time-varying delays, IEEE trans. Syst. man cybernet. 37, No. 3, 713-719 (2007) [16] Wan, L.; Zhou, Q.: Convergence analysis of stochastic hybrid bidirectional associative memory neural networks with delays, Phys. lett. A 370, 423-432 (2007) [17] Zhou, Q.; Sun, J.; Chen, G.: Global exponential stability and periodic oscillations of reaction – diffusion BAM neural networks with periodic coefficients and general delays, Int. J. Bifurc. chaos 17, No. 1, 129-142 (2007) · Zbl 1116.35303 · doi:10.1142/S0218127407017215 [18] L. Sheng, H. Yang, Novel global robust exponential stability criterion for uncertain BAM neural networks with time-varying delays, Chaos, Solitons Fract., in press, doi:10.1016/j.chaos.2007.09.098. [19] Song, Q.; Wang, Z.: A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays, Phys. lett. A 368, 134-145 (2007) [20] Hu, S.; Wang, J.: Global stability of a class of discrete-time recurrent neural networks, IEEE trans. Circ. syst. I 49, No. 8, 1104-1117 (2002) [21] M. Liu, Global asymptotic stability analysis of discrete-time Cohen – Grossberg neural networks based on interval systems, Nonlinear Anal., in press, doi:10.1016/j.na.2007.08.019. [22] Xiong, W.; Cao, J.: Global exponential stability of discrete-time Cohen – Grossberg neural networks, Neurocomputing 64, 433-446 (2005) [23] Wang, L.; Xu, Z.: Sufficient and necessary conditions for global exponential stability of discrete-time recurrent neural networks, IEEE trans. Circ. syst. I 53, No. 6, 1373-1380 (2006) [24] He, W.; Cao, J.: Stability and bifurcation of a class of discrete-time neural networks, Appl. math. Modell. 31, 2111-2122 (2007) · Zbl 1141.93038 · doi:10.1016/j.apm.2006.08.006 [25] Ozcan, N.; Arik, S.: Global robust stability analysis of neural networks with multiple time delays, IEEE trans. Circ. syst. I 53, No. 1, 166-176 (2006) [26] Shen, T.; Zhang, Y.: Improved global robust stability criteria for delayed neural networks, IEEE trans. Circ. syst. II 54, No. 8, 715-719 (2007) [27] Rong, L.: LMI-based criteria for robust stability of Cohen – Grossberg neural networks with delay, Phys. lett. A 339, 63-73 (2005) · Zbl 1137.93401 · doi:10.1016/j.physleta.2005.03.023 [28] Chen, T.; Rong, L.: Robust global exponential stability of Cohen – Grossberg neural networks with time delay, IEEE trans. Neural netw. 15, No. 1, 203-206 (2004) [29] Yuan, K.; Cao, J.; Li, H.: Robust stability of switched Cohen – Grossberg neural networks with mixed time-varying delays, IEEE trans. Syst. man cybernet. 36, No. 6, 1356-1363 (2006) [30] Cao, J.; Wang, J.: Global asymptotic and robust stability of recurrent neural networks with time delays, IEEE trans. Circ. syst. I 52, No. 2, 417-426 (2005) [31] Li, C.; Liao, X.: Global robust stability criteria for interval delayed neural networks via an LMI approach, IEEE trans. Circ. syst. II 53, No. 9, 901-905 (2006) [32] Liu, B.; Liu, X. Z.: Robust stability of uncertain discrete impulsive systems, IEEE trans. Circ. syst. II 54, No. 5, 455-459 (2007) [33] Boyd, S.; Ghaoui, L. E.; Feron, E.; Balakrishnan, V.: Linear matrix inequalities in system and control theory, (1994) [34] Khargonekar, P. P.; Petersen, I. R.; Zhou, K.: Robust stabilization of uncertain linear systems: quadratic stability and H$\infty$ control theory, IEEE trans. Autom. control 35, No. 3, 356-361 (1990) · Zbl 0707.93060 · doi:10.1109/9.50357