Skip to main content
Erschienen in: Neural Computing and Applications 12/2018

16.11.2016 | Original Article

New exponential passivity of BAM neural networks with time-varying delays

verfasst von: J. Thipcha, P. Niamsup

Erschienen in: Neural Computing and Applications | Ausgabe 12/2018

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this paper, the exponential passivity for bidirectional associative memory (BAM) neural networks with time-varying delays is considered. In our study, the lower and upper bounds of the activation functions are allowed to be either positive, negative or zero. By constructing new and improved Lyapunov–Krasovskii functional and introducing free-weighting matrices, a new and improved delay-dependent exponential passivity criterion for BAM neural networks with time-varying delays is derived in the form of linear matrix inequality (LMI). A numerical example is given to show that the derived condition is less conservative than some existing results given in the literature.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Boyd S, El Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory, vol. 15 of SIAM studies in applied mathematics. SIAM, PhiladephiaCrossRefMATH Boyd S, El Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory, vol. 15 of SIAM studies in applied mathematics. SIAM, PhiladephiaCrossRefMATH
2.
Zurück zum Zitat Cao J, Xiao M (2007) Stability and Hopf bifurcation in a simplified BAM neural network with two time delays. IEEE Trans Neural Netw 18(2):416–430MathSciNetCrossRef Cao J, Xiao M (2007) Stability and Hopf bifurcation in a simplified BAM neural network with two time delays. IEEE Trans Neural Netw 18(2):416–430MathSciNetCrossRef
3.
Zurück zum Zitat Ding K, Huang N-J, Xu X (2007) Global robust exponential stability of interval BAM neural networks with mixed delays under uncertainty. Neural Proc Lett 25:127–141CrossRef Ding K, Huang N-J, Xu X (2007) Global robust exponential stability of interval BAM neural networks with mixed delays under uncertainty. Neural Proc Lett 25:127–141CrossRef
4.
Zurück zum Zitat Du Y, Zhong S, Zhou N, Nie L, Wang W (2013) Exponential passivity of BAM neural networks with time-varying delays. Appl Math Comput 221:727–740MathSciNetMATH Du Y, Zhong S, Zhou N, Nie L, Wang W (2013) Exponential passivity of BAM neural networks with time-varying delays. Appl Math Comput 221:727–740MathSciNetMATH
5.
6.
Zurück zum Zitat Hu L, Liu H, Zhao Y (2009) New stability criteria for BAM neural networks with time-varying delays. Neurocomputing 72:3245–3252CrossRef Hu L, Liu H, Zhao Y (2009) New stability criteria for BAM neural networks with time-varying delays. Neurocomputing 72:3245–3252CrossRef
7.
Zurück zum Zitat Kharitonov VL (2013) Time-delay systems: Lyapunov functionals and matrices. Birkhauser, DordrechtCrossRefMATH Kharitonov VL (2013) Time-delay systems: Lyapunov functionals and matrices. Birkhauser, DordrechtCrossRefMATH
8.
Zurück zum Zitat Kosko B (1992) Neural networks and fuzzy systems a dynamical system approach to machine intelligence. Prentice-Hall, Englewood CliffsMATH Kosko B (1992) Neural networks and fuzzy systems a dynamical system approach to machine intelligence. Prentice-Hall, Englewood CliffsMATH
9.
Zurück zum Zitat Kosko B (1987) Adaptive bidirectional associative memories. Appl Opt 26:4947–4960CrossRef Kosko B (1987) Adaptive bidirectional associative memories. Appl Opt 26:4947–4960CrossRef
11.
Zurück zum Zitat Kwon OM, Lee SM, Park JH, Cha EJ (2012) New approaches on stability criteria for neural networks with time varying delays. Appl Math Comput 218:9953–9964MathSciNetMATH Kwon OM, Lee SM, Park JH, Cha EJ (2012) New approaches on stability criteria for neural networks with time varying delays. Appl Math Comput 218:9953–9964MathSciNetMATH
12.
Zurück zum Zitat Kwon OM, Lee SM, Park JH (2012) On improved passivity criteria of uncertain neural networks with time-varying delays. Nonlinear Dyn 67:1261–1271MathSciNetCrossRefMATH Kwon OM, Lee SM, Park JH (2012) On improved passivity criteria of uncertain neural networks with time-varying delays. Nonlinear Dyn 67:1261–1271MathSciNetCrossRefMATH
13.
Zurück zum Zitat Liao X, Yu J, Chen G (2002) Novel stability criteria for bidirectional associative memory neural networks with time delays. Int J Circ Theory Appl 30:519–546CrossRefMATH Liao X, Yu J, Chen G (2002) Novel stability criteria for bidirectional associative memory neural networks with time delays. Int J Circ Theory Appl 30:519–546CrossRefMATH
14.
Zurück zum Zitat Mahmoud MS, Xia Y (2010) LMI-based exponential stability criterion for bidirectional associative memory neural networks. Neurocomputing 74:284–290CrossRef Mahmoud MS, Xia Y (2010) LMI-based exponential stability criterion for bidirectional associative memory neural networks. Neurocomputing 74:284–290CrossRef
15.
Zurück zum Zitat Mathiyalagan K, Sakthivel R, Anthoni SM (2012) New robust passivity criteria for stochastic fuzzy BAM neural networks with time-varying delays. Commun Nonlinear Sci Numer Simul 17:1392–1407MathSciNetCrossRefMATH Mathiyalagan K, Sakthivel R, Anthoni SM (2012) New robust passivity criteria for stochastic fuzzy BAM neural networks with time-varying delays. Commun Nonlinear Sci Numer Simul 17:1392–1407MathSciNetCrossRefMATH
16.
Zurück zum Zitat Peng S (2010) Global attractive periodic solutions of BAM neural networks with continuously distributed delays in the leakage terms. Nonlinear Anal Real World Appl 11:2141–2151MathSciNetCrossRefMATH Peng S (2010) Global attractive periodic solutions of BAM neural networks with continuously distributed delays in the leakage terms. Nonlinear Anal Real World Appl 11:2141–2151MathSciNetCrossRefMATH
17.
Zurück zum Zitat Phat VN, Trinh H (2013) Design of \(H_{\infty }\) control of neural networks with time-varying delays. Neural Comput Appl 23:323–331CrossRef Phat VN, Trinh H (2013) Design of \(H_{\infty }\) control of neural networks with time-varying delays. Neural Comput Appl 23:323–331CrossRef
18.
Zurück zum Zitat Raja R, Karthik Raja U, Samidurai R, Leelamani A (2014) Passivity analysis for uncertain discrete-time stochastic BAM neural networks with time-varying delays. Neural Comput Appl 25:751–766CrossRefMATH Raja R, Karthik Raja U, Samidurai R, Leelamani A (2014) Passivity analysis for uncertain discrete-time stochastic BAM neural networks with time-varying delays. Neural Comput Appl 25:751–766CrossRefMATH
19.
Zurück zum Zitat Rao VSH, Phaneendra BRM (1999) Global dynamics of bidirectional associative memory neural networks involving transmission delays and dead zone. Neural Netw 12(3):455–465CrossRef Rao VSH, Phaneendra BRM (1999) Global dynamics of bidirectional associative memory neural networks involving transmission delays and dead zone. Neural Netw 12(3):455–465CrossRef
20.
Zurück zum Zitat Sakthivel R, Arunkumar A, Mathiyalagan K, Marshal S (2011) Anthoni, Robust passivity analysis of fuzzy Cohen Grossberg BAM neural networks with time-varying delays. Appl Math Comput 218:3799–3809MathSciNetMATH Sakthivel R, Arunkumar A, Mathiyalagan K, Marshal S (2011) Anthoni, Robust passivity analysis of fuzzy Cohen Grossberg BAM neural networks with time-varying delays. Appl Math Comput 218:3799–3809MathSciNetMATH
21.
Zurück zum Zitat Samidurai R, Sakthivel R, Anthoni SM (2009) Global asymptotic stability of BAM neural networks with mixed delays and impulses. Appl Math Comput 212:113–119MathSciNetMATH Samidurai R, Sakthivel R, Anthoni SM (2009) Global asymptotic stability of BAM neural networks with mixed delays and impulses. Appl Math Comput 212:113–119MathSciNetMATH
22.
Zurück zum Zitat Singh YP, Yadav VS, Gupta A, Khare A (2005–2009) Bidirection associative memory neural networks method in the character recognition. J Theor Appl Inf Tech 5:382–386 Singh YP, Yadav VS, Gupta A, Khare A (2005–2009) Bidirection associative memory neural networks method in the character recognition. J Theor Appl Inf Tech 5:382–386
23.
Zurück zum Zitat Thipcha J, Niamsup P (2013) Global exponential stability criteria for bidirectional associative memory neural networks with time-varying delays. Abstr Appl Anal 2013:1–13MathSciNetCrossRefMATH Thipcha J, Niamsup P (2013) Global exponential stability criteria for bidirectional associative memory neural networks with time-varying delays. Abstr Appl Anal 2013:1–13MathSciNetCrossRefMATH
24.
Zurück zum Zitat Thuan MV, Phat VN (2012) New criteria for stability and stabilization of neural networks with mixed interval time-varying delays. Vietnam J Math 40:79–93MathSciNetMATH Thuan MV, Phat VN (2012) New criteria for stability and stabilization of neural networks with mixed interval time-varying delays. Vietnam J Math 40:79–93MathSciNetMATH
25.
Zurück zum Zitat Tu Z, Wanga L, Zha Z, Jian J (2013) Global dissipativity of a class of BAM neural networks with time-varying and unbound delays. Commun Nonlinear Sci Numer Simul 18:2562–2570MathSciNetCrossRefMATH Tu Z, Wanga L, Zha Z, Jian J (2013) Global dissipativity of a class of BAM neural networks with time-varying and unbound delays. Commun Nonlinear Sci Numer Simul 18:2562–2570MathSciNetCrossRefMATH
26.
Zurück zum Zitat Wang B, Jian J, Guo C (2008) Global exponential stability of a class of BAM networks with time-varying delays and continuously distributed delays. Neurocomputing 71:495–501CrossRef Wang B, Jian J, Guo C (2008) Global exponential stability of a class of BAM networks with time-varying delays and continuously distributed delays. Neurocomputing 71:495–501CrossRef
27.
Zurück zum Zitat Wang H, Song Q, Duan C (2010) LMI criteria on exponential stability of BAM neural networks with both time-varying delays and general activation functions. Math Comput Simul 81:837–850MathSciNetCrossRefMATH Wang H, Song Q, Duan C (2010) LMI criteria on exponential stability of BAM neural networks with both time-varying delays and general activation functions. Math Comput Simul 81:837–850MathSciNetCrossRefMATH
28.
Zurück zum Zitat Zeng H-B, He Y, Wua M, Xiao S-P (2011) Passivity analysis for neural networks with a time-varying delay. Neurocomputing 74:730–734CrossRef Zeng H-B, He Y, Wua M, Xiao S-P (2011) Passivity analysis for neural networks with a time-varying delay. Neurocomputing 74:730–734CrossRef
29.
Zurück zum Zitat Zhang D, Yu L (2012) Passivity analysis for discrete-time switched neural networks with various activation functions and mixed time delay. Nonlinear Dyn 67:403–411MathSciNetCrossRefMATH Zhang D, Yu L (2012) Passivity analysis for discrete-time switched neural networks with various activation functions and mixed time delay. Nonlinear Dyn 67:403–411MathSciNetCrossRefMATH
30.
Zurück zum Zitat Zhang XM, Han QL (2009) New Lyapunov–Krasovskii functionals for global asymptotic stability of delayed neural networks. IEEE Trans Neural Netw 20:533–539CrossRef Zhang XM, Han QL (2009) New Lyapunov–Krasovskii functionals for global asymptotic stability of delayed neural networks. IEEE Trans Neural Netw 20:533–539CrossRef
31.
Zurück zum Zitat Zhang XM, Han QL (2011) Global asymptotic stability for a class of generalized neural networks with interval time-varying delays. IEEE Trans Neural Netw 22:1180–1192CrossRef Zhang XM, Han QL (2011) Global asymptotic stability for a class of generalized neural networks with interval time-varying delays. IEEE Trans Neural Netw 22:1180–1192CrossRef
32.
Zurück zum Zitat Zhang XM, Han QL (2013) Novel delay-derivative-dependent stability criteria using new bounding techniques. Int J Robust Nonlinear Control 23:1419–1432MathSciNetCrossRefMATH Zhang XM, Han QL (2013) Novel delay-derivative-dependent stability criteria using new bounding techniques. Int J Robust Nonlinear Control 23:1419–1432MathSciNetCrossRefMATH
33.
Zurück zum Zitat Zhang XM, Han QL (2014) Global asymptotic stability analysis for delayed neural networks using a matrix-based quadratic convex approach. Neural Newtw 54:57–69CrossRefMATH Zhang XM, Han QL (2014) Global asymptotic stability analysis for delayed neural networks using a matrix-based quadratic convex approach. Neural Newtw 54:57–69CrossRefMATH
34.
Zurück zum Zitat Zhang Z, Liu K, Yang Y (2012) New LMI-based condition on global asymptotic stability concerning BAM neural networks of neutral type. Neurocomputing 81:24–32CrossRef Zhang Z, Liu K, Yang Y (2012) New LMI-based condition on global asymptotic stability concerning BAM neural networks of neutral type. Neurocomputing 81:24–32CrossRef
35.
Zurück zum Zitat Zhao Z, Liu F, Xie X, Liu X, Tang Z (2013) Asymptotic stability of bidirectional associative memory neural networks with time-varying delays via delta operator approach. Neurocomputing 117:40–46CrossRef Zhao Z, Liu F, Xie X, Liu X, Tang Z (2013) Asymptotic stability of bidirectional associative memory neural networks with time-varying delays via delta operator approach. Neurocomputing 117:40–46CrossRef
36.
Zurück zum Zitat Zhu S, Shena Y, Chen G (2010) Exponential passivity of neural networks with time-varying delay and uncertainty. Phys Lett A 375:136–142MathSciNetCrossRef Zhu S, Shena Y, Chen G (2010) Exponential passivity of neural networks with time-varying delay and uncertainty. Phys Lett A 375:136–142MathSciNetCrossRef
Metadaten
Titel
New exponential passivity of BAM neural networks with time-varying delays
verfasst von
J. Thipcha
P. Niamsup
Publikationsdatum
16.11.2016
Verlag
Springer London
Erschienen in
Neural Computing and Applications / Ausgabe 12/2018
Print ISSN: 0941-0643
Elektronische ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-016-2657-1

Weitere Artikel der Ausgabe 12/2018

Neural Computing and Applications 12/2018 Zur Ausgabe