488Accesses
Abstract
In this paper, the finite-time stability problem is considered for a class of stochastic Cohen–Grossberg neural networks (CGNNs) with Markovian jumping parameters and distributed time-varying delays. Based on Lyapunov–Krasovskii functional and stability analysis theory, a linear matrix inequality approach is developed to derive sufficient conditions for guaranteeing the stability of the concerned system. It is shown that the addressed stochastic CGNNs with Markovian jumping and distributed time varying delays are finite-time stable. An illustrative example is provided to show the effectiveness of the developed results.
This is a preview of subscription content,log in via an institution to check access.
Access this article
Subscribe and save
- Get 10 units per month
- Download Article/Chapter or eBook
- 1 Unit = 1 Article or 1 Chapter
- Cancel anytime
Buy Now
Price includes VAT (Japan)
Instant access to the full article PDF.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Cohen M, Grossberg S (1983) Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans Syst Man Cybern 3:815–826
Wu X, Tang Y, Zhang W (2014) Stability analysis of switched stochastic neural networks with time-varying delays. Neural Netw 51:39–49
Zhu Q, Cao J (2010) Robust exponential stability of Markovian jump impulsive stochastic Cohen–Grossberg neural networks with mixed time delays. IEEE Trans Neural Netw 21:1314–1325
Chen P, Hiang C, Liang X (2010) Stochastic stability of Cohen–Grossberg neural networks with unbounded distributed delays. Electron J Differ Equ 42:1–11
Chen Z, Zhad D, Ruan J (2007) Dynamic analysis of high-order Cohen–Grossberg neural networks with time delay. Chaos Solitons Fractals 32:1538–1546
Balasubramaniam P, Syed Ali M (2010) Robust exponential stability of uncertain fuzzy Cohen–Grossberg neural networks with time-varying delays. Fuzzy Set Syst 161:608–618
Haykin S (1994) Neural networks: a comprehensive foundation. Prentice-Hall, Upper Saddle River
Balasubramaniam P, Syed Ali M, Arik S (2015) Global asymptotic stability of stochastic fuzzy cellular neural networks with multiple time-varying delays. Expert Syst Appl 37:7737–7744
Cheng J, Zhu H, Ding Y, Zhong S, Zhong Q (2014) Stochastic finite-time boundedness for Markovian jumping neural networks with time-varying delays. Appl Math Comput 242:281–295
Park MJ, Kwon OM, Park JuH, Lee SM, Cha EJ (2012) Synchronization criteria for coupled stochastic neural networks with time-varying delays and leakage delay. J Franklin Inst 349:1699–1720
Kwon OM, Lee SM, Park JuH (2010) Improved delay-dependent exponential stability for uncertain stochastic neural networks with time-varying delays. Phys Lett A 374:1232–1241
Shi P, Zhang Y, Agarwal RK (2015) Stochastic finite-time state estimation for discrete time-delay neural networks with Markovian jumps. Neurocomputing 151:168–174
Zhang H, Wang Y (2008) Stability analysis of Markovian jumping stochastic Cohen–Grossberg neural networks with mixed time delays. IEEE Trans Neural Netw 19:366–370
Shan QH, Wang Z (2012) Improved stability results for stochastic Cohen–Grossberg neural networks with discrete and distributed delays. Neural Process Lett 35:103–129
Bao H (2016) Existence and exponential stability of periodic solution for BAM fuzzy Cohen–Grossberg neural networks with mixed delays. Neural Process Lett 43:871–885
Du Y, Xu R (2015) Multistability and multiperiodicity for a class of Cohen–Grossberg BAM neural networks with discontinuous activation functions and time delays. Neural Process Lett 42:417–435
Wang Z, Liu Y, Li M, Liu X (2006) Stability analysis for stochastic Cohen–Grossberg neural networks with mixed time delays. IEEE Trans Neural Netw 17:814–820
Dong M, Zhang H, Wang Y (2009) Dynamics analysis of impulsive stochastic Cohen–Grossberg neural networks with Markovian jumping and mixed time delays. Neurocomputing 72:1999–2004
Chen M, Yang X, Shen H, Yao F (2016) Finite-time asynchronous\(H_\infty \) control for Markov jump repeated scalar non-linear systems with input constraints. Appl Math Comput 275:172–180
Li F, Shen H (2015) Finite-time\(H_\infty \) synchronization control for semi-Markov jump delayed neural networks with randomly occurring uncertainties. Neurocomputing 166:447–454
Zhu Q, Cao J, Hayat T, Alsaadi F (2015) Robust stability of Markovian jump stochastic neural networks with time delays in the leakage terms. Neural Process Lett 41:1–27
Chen M, Zhang L, Shen H (2016) Resilient\(H_\infty \) filtering for discrete-time uncertain Markov jump neural networks over a finite-time interval. Neurocomputing 185:212–219
Syed Ali M (2015) Stability of Markovian jumping recurrent neural networks with discrete and distributed time-varying delays. Neurocomputing 149:1280–1285
Kao YG, Xie J, Wang CH (2014) Stabilisation of mode-dependent singular Markovian jump systems with generally uncertain transition rates. Appl Math Comput 245:243–254
Kao YG, Wang CH, Xie J, Karimi HR, Li W (2014)\(H_\infty \) sliding mode control for uncertain neutral-type stochastic systems with Markovian jumping parameters. Inf Sci 314:200–211
Liu H, Shen Y, Zhao XD (2013) Finite-time stabilization and boundedness of switched linear system under state-dependent switching. J Franklin Inst 350:541–555
Chen GP, Yang Y (2014) Finite-time stability of switched positive linear systems. Int J Robust Nonlinear Control 24:179–190
Zhang JF, Yang Y (2014) Robust finite-time stability and stabilization of switched positive systems. IET Control Theory Appl 8:67–75
He SP, Liu F (2013) Finite-time boundedness of uncertain time-delayed neural network with Markovian jumping parameters. Neurocomputing 103:87–92
Wang S, Ma C, Zeng M, Yu Z, Liu Y (2014) Finite-time boundedness of uncertain switched time-delay neural networks with mode-dependent average dwell time. In: IEEE transactions on control conference (CCC), pp 4078–4083
Zhang YQ, Shi P, Nguang SK, Zhang JH, Karimi HR (2014) Finite-time boundedness for uncertain discrete neural networks with time-delays and Markovian jumps. Neurocomputing 140:1–7
Cheng J, Zhong S, Zhong Q, Zhu H, Du YH (2014) Finite-time boundedness of state estimation for neuralnetworks with time-varying delays. Neurocomputing 129:257–264
Cheng J, Zhu H, Zhong S, Zeng Y, Hou L (2014) Finite-time\(H_\infty \) filtering for a class of discrete-time Markovian jump systems with partly unknown transition probabilities. Int J Adapt Control Signal Process 28:1024–1042
Franceschelli M, Giua A, Pisano A, Usai E (2013) Finite-time consensus for switching network topologies with disturbances. Nonlinear Anal 10:83–93
Gu K, Kharitonov VL, Chen J (2003) Stability of time delay systems. Birkhuser, Boston
Ahn CK (2010) An\(H_\infty \) approach to stability analysis of switched Hopfield neural networks with time-delay. Nonlinear Dyn 60:703–711
Ahn CK (2011) Switched exponential state estimation of neural networks based on passivity theory. Nonlinear Dyn 67:573–586
Author information
Authors and Affiliations
Department of Computer Engineering, Faculty of Engineering, Istanbul University, Avcilar, 34320, Istanbul, Turkey
Emel Arslan
Department of Mathematics, Thiruvalluvar University, Vellore, Tamil Nadu, 632 115, India
M. Syed Ali & S. Saravanan
- Emel Arslan
You can also search for this author inPubMed Google Scholar
- M. Syed Ali
You can also search for this author inPubMed Google Scholar
- S. Saravanan
You can also search for this author inPubMed Google Scholar
Corresponding author
Correspondence toM. Syed Ali.
Rights and permissions
About this article
Cite this article
Arslan, E., Ali, M.S. & Saravanan, S. Finite-Time Stability of Stochastic Cohen–Grossberg Neural Networks with Markovian Jumping Parameters and Distributed Time-Varying Delays.Neural Process Lett46, 71–81 (2017). https://doi.org/10.1007/s11063-016-9574-2
Published:
Issue Date:
Share this article
Anyone you share the following link with will be able to read this content:
Sorry, a shareable link is not currently available for this article.
Provided by the Springer Nature SharedIt content-sharing initiative