Top

Neural Computing and Applications

Published in:

01-05-2013 | Original Article

Two algebraic criteria for input-to-state stability of recurrent neural networks with time-varying delays

Authors: Song Zhu, Yi Shen

Published in: Neural Computing and Applications | Issue 6/2013

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

This paper presents two algebraic criteria for the input-to-state stability of recurrent neural networks with time-varying delays. The criteria which also ensure global exponential stability when the input u(t) is equal to 0 and is easy to be verified only with the connection weights of the recurrent neural networks. Two numerical examples are given to demonstrate the effectiveness of the proposed criteria.

previous article A novel image mining technique for classification of mammograms using hybrid feature selection

next article State of charge neural computational models for high energy density batteries in electric vehicles

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

inform now

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!

inform now

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!

inform now

Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Nat Acad Sci USA 79:2554−2558MathSciNetCrossRef

Chua LO, Yang L (1988) Cellular neural networks: Theory. IEEE Trans Circuits Syst 35(10):1257–1272MathSciNetMATHCrossRef

Cohen MA, Grossberg S (1983) Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans Syst Man Cybern 13(5):815–821MathSciNetMATHCrossRef

Arik S (2002) An analysis of global asymptotic stability of delayed cellular neural networks. IEEE Trans Neural Netw 13(5):1239–1242CrossRef

Cao J, Yuan K, Li H (2006) Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays. IEEE Trans Neural Netw 17(6):1646–1651CrossRef

Cao J, Wang J (2003) Global asymptotic satbility of a general class of recurrent neural networks with time varying delays. IEEE Trans Neural Netw 50(1):34–44MathSciNet

He Y, Wu M, She J (2006) Delay-dependent exponential stability for delayed neural networks with time-varying delay. IEEE Trans Circuits Syst II Exp Briefs 53(7):553–557CrossRef

Meng X, Tian M, Hu S (2011) Stability analysis of stochastic recurrent neural networks with unbounded time-varying delays. Neurocomputing 74(6):949–953CrossRef

Liao X, Wang J (2003) Algebraic criteria for global exponential stability of cellular neural networks with multiple time delays. IEEE Trans Circuits Syst I Fundam Theory Appl 50(2):268–275MathSciNetCrossRef

10.

Liao X, Wang J, Zeng Z (2005) Global asymptotic stability and global exponential stability of delayed cellular neural networks. IEEE Trans Circuits Syst II Exp Briefs 52(7):403–409CrossRef

11.

Li C, Liao X (2004) Global robust asymptotical stability of multi-delayed interval neural networks: an LMI approach. Phys Lett A 328(6):452–462MathSciNetMATHCrossRef

12.

Xu S, Lam J, Ho DWC (2006) A new LMI condition for delay dependent asymptotic stability of delayed Hopfield neural networks. IEEE Trans Circuits Syst II Exp Briefs 53(3):230–234CrossRef

13.

Chen H, Zhang Y, Hu P (2010) Novel delay-dependent robust stability criteria for neutral stochastic delayed neural networks. Neurocomputing 73(13–15):2554–2561CrossRef

14.

Zhang H, Wang Z, Liu D (2008) Global asymptotic stability of recurrent neural networks with multiple time-varying delays. IEEE Trans Neural Netw 19(5):855–873MathSciNetCrossRef

15.

Zeng Z, Wang J (2006) Complete stability of cellular neural networks with time-varying delays. IEEE Trans Circuits Syst I Reg Papers 53(4):944–955MathSciNetCrossRef

16.

Zeng Z, Wang J, Liao X (2003) Global exponential stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans Circuits Syst I Fundam Theory Appl 50(10):1353–1358MathSciNetCrossRef

17.

Shen Y, Wang J (2008) An improved algebraic criterion for global exponential stability of recurrent neural networks with time-varying delays. IEEE Trans Neural Netw 19(3):528–531CrossRef

18.

Song Q (2008) Exponential stability of recurrent neural networks with both time varying delays and general activation functions via LMI approach. Neurocomputing 71(13–15):2823–2830CrossRef

19.

Liang J, Wang Z, Liu X (2009) State estimation for coupled uncertain stochastic networks with missing measurements and time-varying times: the discrete-time case. IEEE Trans Neural Netw 20(5):781–793CrossRef

20.

Chen T, Rong L (2004) Robust global exponential stability of Cohen-Grossberg neural networks with time delays. IEEE Trans Neural Netw 15(1):203–206MathSciNetCrossRef

21.

Xu S, Lam J, Ho DWC, Zou Y (2004) Global robust exponential stability analysis for interval recurrent neural networks. Phys. Lett. A, 352(2):124–133CrossRef

22.

Forti M, Nistri P, Papini P (2005) Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain. IEEE Trans Neural Netw 16(6):1449–1463CrossRef

23.

Huang H, Qu Y, Li H (2005) Robust stability analysis of switched Hopfield neural networks with time-varying delay under uncertainty. Phys Lett A 345:345–354MATHCrossRef

24.

Shen Y, Wang J (2009) Almost sure exponential stability of recurrent neural networks with Markovian switching. IEEE Trans Neural Netw 20(5):840–855MathSciNetCrossRef

25.

Wang Z, Liu Y, Liu X (2009) State estimation for jumping recurrent neural networks with discrete and distributed delays. Neural Netw 22(1):41–48CrossRef

26.

Zhu S, Shen Y, Chen G (2010) Exponential passivity of neural networks with time-varying delay and uncertainty. Phys Lett A 375:136–142MathSciNetMATHCrossRef

27.

Sontag ED (1989) Smooth stabilization implies corpime factorization. IEEE Trans Automat Control 34:435–443MathSciNetMATHCrossRef

28.

Sontag ED (2006) Input to state stability: basic concepts and results. In: Nistri N, Stefani G (eds) Nonlinear Optimal Control Theory, pp 163–220

29.

Sontag ED, Wang Y (1996) New characterizations of input to state stability. IEEE Trans Autom Control (41):1283–1294

30.

Jiang Z, Wang Y (2001) Input-to-state stability for discrete-time nonlinear systems. Automatica (37):857–869

31.

Cao C, Teel AR (2009) Characterizations of input-to-state stability for hybrid systems. Syst. Control Lett. 58:47–53CrossRef

32.

Huang L, Mao X (2009) On input-to-state stability of stochastic retarded systems with Markovian switching. IEEE Trans Automat Control 54 (8):1898–1902MathSciNetCrossRef

33.

Fridman E, Dambrine M, Yeganefar N (2008) On input-to-state stability of systems with time-delay: A matrix inequalities approach. Automatica (44):2364–2369

34.

Sontag ED (1995) On the input to state stability property. Eur J Control 1:1–24

35.

Sanchez EN, Perez JP (1999) Input-to-state stability(ISS) analysis for dynamic neural networks. IEEE Trans Circuits Syst I Fundam Theory Appl 46(11):1395–1398MathSciNetMATHCrossRef

36.

Guo Y (2008) New results on input-to-state convergence for recurrent neural networks with variable inputs. Nonlinear Anal RWA. (9):1558–1566

37.

Yu W, Li X (2001) Some stability properties of dynamic neural networks. IEEE Trans Circuits Syst I Fundam Theory Appl 48(2):256–259MATHCrossRef

38.

Ahn CK (2010) Passive learning and input-to-state stability of switched Hopfield neural networks with time-delay. Inform Sci (180):4582–4594

Title: Two algebraic criteria for input-to-state stability of recurrent neural networks with time-varying delays
Authors: Song Zhu
Yi Shen
Publication date: 01-05-2013
Publisher: Springer-Verlag
Published in: Neural Computing and Applications / Issue 6/2013
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI: https://doi.org/10.1007/s00521-012-0882-9

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Springer Professional "Wirtschaft+Technik"

Other articles of this Issue 6/2013

Emotion recognition improvement using normalized formant supplementary features by hybrid of DTW-MLP-GMM model

Associate learning and correcting in a memristive neural network

Artificial neural network models for lot-sizing problem: a case study

Rule-based Mamdani type fuzzy logic model for the prediction of compressive strength of silica fume included concrete using non-destructive test results

State of charge neural computational models for high energy density batteries in electric vehicles

Designing an algorithm for evaluating decision-making units based on neural weighted function

Premium Partner