Skip to main content

Advertisement

SpringerLink
Log in

\(H_\infty \) state estimation of stochastic neural networks with mixed time-varying delays

  • Focus
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

This paper is concerned with \(H_\infty \) state estimation problem of stochastic neural networks with discrete interval and distributed time-varying delays. The time-varying delay is need to be bounded and continuous. By constructing a suitable Lyapunov–Krasovskii functional with triple integral terms and linear matrix inequality technique, the delay-dependent criteria are conferred so that the error system is stochastically asymptotically mean-square stable with \(H_\infty \) performance. The desired estimator gain matrix can be characterized in terms of the solution to linear matrix inequalities, which can be easily solved by some standard numerical algorithms. Numerical simulations are given to demonstrate the effectiveness of the proposed method. The results are also compared with existing methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Balasubramaniam P, Syed Ali M (2011) Stability analysis of Takagi-Sugeno fuzzy Cohen Grossberg BAM neural networks with discrete and distributed time-varying delays. Math Comput Model 53:151–160

    Article  MathSciNet  MATH  Google Scholar 

  • Blythea S, Mao X, Liao X (2001) Stability of stochastic delay neural networks. Commun Nonlinear Sci Numer Simulat 16:2907–2916

    Google Scholar 

  • Boyd B, Ghoui LE, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, Philadephia

    Book  Google Scholar 

  • Chen H (2013) New delay-dependent stability criteria for uncertain stochastic neural networks with discrete interval and distributed delays. Neurocomputing 101:1–9

    Article  Google Scholar 

  • Chen Y, Zheng W (2014) Exponential \(H_\infty \) filtering for stochastic Markovian jump systems with time delays. Int. J. Robust. N onlinear C ontrol 24(4):625–643

  • Gu K, Kharitonov VL, Chen J (2003) Stability of time delay systems. Birkhuser, Boston

    Book  MATH  Google Scholar 

  • Haykin S (1994) Neural networks: a comprehensive foundation. Prentice Hall, New York 1994

    MATH  Google Scholar 

  • Hua M, Caia Y, Nia J, Fei J (2015) Delay-dependent \(H_\infty \) filtering for discrete-time fuzzy stochastic systems with mixed delays and sector-bounded nonlinearity. J Franklin Inst. doi:10.1016/j.jfranklin.2014.11.009

    Google Scholar 

  • Huang H, Feng G, Cao J (2010) State estimation for static neural networks with time-varying delay. Neural Netw 23:1202–1207

    Article  Google Scholar 

  • Huang B, Zhang H, Gong D, Wang J (2015) Synchronization analysis for static neural networks with hybrid couplings and time delays. Neurocomputing 148:288–293

    Article  Google Scholar 

  • Jiao T, Zong G, Zheng W (2013) New stability conditions for GRNs with neutral delay. Soft Comput 17:703–712

    Article  MATH  Google Scholar 

  • Lakshmanan S, Park JH, Rakkiyappan R, Jung HY (2013) State estimator for neural networks with sampled data using discontinuous Lyapunov functional approach. Nonlinear Dyn 73:509–520

    Article  MathSciNet  MATH  Google Scholar 

  • Lakshmanan S, Mathiyalagan K, Park JH, Sakthivel R, Rihan FA (2014) Delay-dependent \(H_\infty \) state estimation of neural networks with mixed time-varying delays. Neurocomputing 129:392–400

    Article  Google Scholar 

  • Lee TH, Lakshmanan S, Park JH, Balasubramaniam P (2013) State estimation for genetic regulatory networks with modedependent leakage delays, timevarying delays, and markovian jumping parameters. IEEE Trans Nanobiosci 12(4):363–375

    Article  Google Scholar 

  • Li T, Song A, Fei S, Wang T (2010) Delay-derivative-dependent stability for delayed neural networks with unbounded distributed delay. IEEE Trans Neural Netw 21:1365–1371

  • Li H, Cheung KC, Lam J, Gao H (2011) Robust stability for interval stochastic neural networks with time-varying discrete and distributed delays. Differ Equ Dyn Syst 19:97–118

    Article  MathSciNet  MATH  Google Scholar 

  • Li H (2013) \(H_\infty \) cluster synchronization and state estimation for complex dynamical networks with mixed time delays. Appl Math Model 37:7223–7244

    Article  MathSciNet  Google Scholar 

  • Liu Y, Lee SM, Kwon OM, Park JH (2014) A study on \(H_\infty \) state estimation of static neural networks with time-varying delays. Appl Math Comput 226:589–597

    MathSciNet  Google Scholar 

  • Mao X (1997) Stochastic differential equations with their applications. Horwood, Chichester

    MATH  Google Scholar 

  • Moon YS, Park P, Kwon WH, Lee YS (2001) Delay-dependent robust stabilization of uncertain state-delayed systems. Int J Control 74(14):1447–1455

    Article  MathSciNet  MATH  Google Scholar 

  • Quan Q, Yang D, Hu H, Cai KY (2010) A new model transformation method and its application to extending a class of stability criteria of neutral type systems. Nonlinear Anal Real World Appl 11(5):3752–3762

    Article  MathSciNet  MATH  Google Scholar 

  • Saravanakumar R, Syed Ali M (2014) \(H_\infty \) state estimation control of neural networks with distributed time-varying delays. In: Proc of the IEEE Int joint Conf (ISCMI2014) ISBN-978-0-7695-5075-6/14:11–14

  • Senthilkumar T, Balasubramaniam P (2011) Robust \(H_\infty \) control for nonlinear uncertain stochastic T-S fuzzy systems with time delays. Appl Math Lett 24:1986–1994

    Article  MathSciNet  MATH  Google Scholar 

  • Shan Q, Zhang H, Yang F, Wang Z (2013) New delay-dependent stability criteria for cohen-grossberg neural networks with multiple time-varying mixed delays. Soft Comput 17:2043–2052

    Article  MATH  Google Scholar 

  • Syed Ali M (2011) Global asymptotic stability of stochastic fuzzy recurrent neural networks with mixed time-varying delays. Chin Phys B 20(8):080201

    Article  Google Scholar 

  • Syed Ali M (2014a) Stability analysis of Markovian Jumping stochastic Cohen-Grossberg neural networks with discrete and distributed time varying delays. Chin Phys B 6:060702

  • Syed Ali M (2014b) Robust stability of stochastic uncertain recurrent neural networks with Markovian jumping parameters and time-varying delays. Int J Mach Learn Cyber 5:13–22

  • Syed Ali M, Marudai M (2011) Stochastic stability of discrete-time uncertain recurrent neural networks with Markovian jumping and time-varying delays. Math Comput Model 54:1979–1988

    Article  MathSciNet  MATH  Google Scholar 

  • Syed Ali M, Saravanakumar R (2014) Novel delay-dependent robust \(H_\infty \) control of uncertain systems with distributed time-varying delays. Appl Math Comput 249:510–520

    MathSciNet  MATH  Google Scholar 

  • Syed Ali M, Saravanakumar R (2014) Improved delay-dependent robust \(H_\infty \) control of an uncertain stochastic system with interval time-varying and distributed delays. Chin Phys B 23(12):120201

    Article  MATH  Google Scholar 

  • Syed Ali M, Saravanakumar R (2015) Augmented Lyapunov approach to \(H_\infty \) state estimation of static neural networks with discrete and distributed time-varying delays. Chin Phys B 24(5): Article ID-050201

  • Syed Ali M, Balasubramaniam P, Lakshmanan S, Rihan FA (2014) Stability criteria for stochastic Takagi-Sugeno fuzzy Cohen-Grossberg BAM neural networks with mixed time-varying delays. Complexity. doi:10.1002/cplx.21642

    Google Scholar 

  • Syed Ali M, Arik S, Saravanakmuar R (2015) Delay-dependent stability criteria of uncertain markovian jump neural networks with discrete interval and distributed time-varying delays. Neurocomputing 158:167–173

    Article  Google Scholar 

  • Syed Ali M, Saravanakumar R, Zhu Q (2015) Less conservative delay-dependent \(H_\infty \) control of uncertain neural networks with discrete interval and distributed time-varying delays. Neurocomputing 166:84–95

    Article  Google Scholar 

  • Tan H, Hua M, Chen J, Fei J (2015) Stability analysis of stochastic Markovian switching static neural networks with asynchronous mode-dependent delays. Neurocomputing 151:864–872

    Article  Google Scholar 

  • Wang Z, Liao X, Mao J, Liu G (2009) Robust stability of stochastic genetic regulatory networks with discrete and distributed delays. Soft Comput 13:1199–1208

    Article  MATH  Google Scholar 

  • Wang J, Jiang H, Hu C (2014) Existence and stability of periodic solutions of discrete-time Cohen Grossberg neural networks with delays and impulses. Neurocomputing 142:542–550

    Article  Google Scholar 

  • Wang H, Yu Y, Wen G (2014) Stability analysis of fractional-order Hopfield neural networks with time delays. Commun Nonlinear Sci Numer Simulat 55:98–109

    MATH  Google Scholar 

  • Wanga T, Dinga Y, Zhanga L, Hao K (2015) Delay-dependent exponential state estimators for stochastic neural networks of neutral type with both discrete and distributed delays. Int J Syst Sci 46:670–680

    Article  MathSciNet  Google Scholar 

  • Wu H, Liao X, Feng W (2012) Mean square stability of uncertain stochastic BAM neural networks with interval time-varying delays. Cogn Neurodyn 6:443–458

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Thiruvalluvar University, Vellore, 632115, Tamil Nadu, India

    R. Saravanakumar & M. Syed Ali

  2. College of Internet of Things Engineering, Hohai University, Changzhou, 213022, China

    Mingang Hua

Authors
  1. R. Saravanakumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Syed Ali
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mingang Hua
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Saravanakumar.

Ethics declarations

Conflict of interest

We declare that, there is no conflict of interest in this paper.

Ethical statement

This paper has not been submitted elsewhere for publications. No data have been fabricated or manipulated to support this paper. Consent to submit has been received from all coauthors.

Additional information

Communicated by S. Deb, T. Hanne and S. Fong.

The work was supported by National Board of Higher Mathematics (NBHM), New Delhi under research project No.2/48/10/2011-R&D-II/865.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Saravanakumar, R., Ali, M.S. & Hua, M. \(H_\infty \) state estimation of stochastic neural networks with mixed time-varying delays. Soft Comput 20, 3475–3487 (2016). https://doi.org/10.1007/s00500-015-1901-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-015-1901-4

Keywords

Search

Navigation