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Equilibrium and Stability Analysis of Takagi-Sugeno Fuzzy Delayed Cohen-Grossberg Neural Networks

Year 2019, Volume: 68 Issue: 2, 1411 - 1426, 01.08.2019

Neyir Ozcan

https://doi.org/10.31801/cfsuasmas.455799
Cited By: 1

Abstract

This paper carries out an investigation into the problem of the global asymptotic stability of the class of Takagi-Sugeno (T-S) fuzzy delayed Cohen-Grossberg neural networks with discrete time delays. A new sufficient criterion for the uniqueness and global asymptotic stability of the equilibrium point for this class of fuzzy neural networks is proposed. The uniqueness of the equilibrium point is proved by using the contradiction method. The stability of the equilibrium point is established by employing a new fuzzy type Lyapunov functional. The obtained stability result is obtained with respect to the nondecreasing and slope-bounded activation functions it can be shown to be independent of time delays. The proposed result can be easily verified by using some commonly used norm properties of matrices.

Keywords

Stability Theory Equilibrium Analysis Cohen-Grossberg Neural Networks Delayed T-S Fuzzy Systems

References

  • Cohen, M.A. and Grossberg, S., Absolute stability and global pattern formation and parallel memory storage by competitive neural networks, IEEE Transactions on Systems, Man and Cybernetics, vol. 13, (1983), 815-821.
  • Li, L. and Jian, J., Exponential convergence and Lagrange stability for impulsive Cohen-Grossberg neural networks with time-varyin delays, Journal of Computational and Applied Mathematics, vol. 277, (2015), 23-35.
  • Yu, S,. Zhang, Z. and Quan, Z., New global exponential stability conditions for inertial Cohen-Grossberg neural networks with time delays, Neurocomputing, vol. 151, (2015), 1446-1454.
  • Liu, Y., Liu, W., Obaid, M. A. and Abbas, I. A., Exponential stability of Markovian jumping Cohen-Grossberg neural networks with mixed mode-dependent time-delays, Neurocomputing, vol. 177, (2016), 409-415.
  • Esteves, S. and Oliveira, J. J., Global asymptotic stability of nonautonomous Cohen-Grossberg neural network models with infinite delays, Applied Mathematics and Computation, vol. 265, (2015), 333-346.
  • Ozcan, N., New conditions for global stability of neutral-type delayed Cohen-Grossberg neural networks, Neural Networks, vol. 106, (2018), 1-7.
  • Du, Y. and Xu, R., Multistability and multiperiodicity for a class of Cohen-Grossberg BAM neural networks with discontinuous activation functions and time delays, Neural Processing Letters, vol. 42, (2015), 417--435.
  • Kao, Y., Wang, C. and Zhang, L., Delay-dependent robust exponential stability of impulsive Markovian jumping reaction-diffusion Cohen-Grossberg neural networks, Neural Processing Letters, vol. 38, (2013), 321--346.
  • Li, R., Cao, J., Alsaedi, A. and Ahmad, B., Passivity analysis of delayed reaction-diffusion Cohen-Grossberg neural networks via Hardy-Poincare inequality, Journal of the Franklin Institute, vol. 354, (2017), 3021--3038.
  • Li, B. and Song, Q., Some new results on periodic solution of Cohen-Grossberg neural network with impulses, Neurocomputing, vol. 177, (2016), 401--408.
  • Nie, X., Zheng, W. X. and Cao, J., Multistability of memristive Cohen-Grossberg neural networks with non-monotonic piecewise linear activation functions and time-varying delays , Neural Networks, vol. 71, (2015), 27--36.
  • Wei, T., Wang, L. and Wang, Y., Existence, uniqueness and stability of mild solutions to stochastic reaction-diffusion Cohen-Grossberg neural networks with delays and Wiener processes, Neurocomputing, vol. 239, (2017), 19-27.
  • Zheng, C.D., Shan, Q. H., Zhang, H. and Wang, Z., On stabilization of stochastic Cohen-Grossberg neural networks with mode-dependent mixed time-delays and Markovian switching, IEEE Transactions on Neural Networks and Learning Systems, vol. 24, (2013), 800--811.
  • Xu, C. and Zhang, Q., On antiperiodic solutions for Cohen-Grossberg shunting inhibitory neural networks with time-varying delays and impulses, Neural Computation, vol. 26, (2014), 2328--2349. Zhu, Q.X. and Cao, J.D., Robust exponential stability of Markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays, IEEE Transactions on Neural Networks and Learning Systems, vol. 21, (2010), 1314--1325.
  • Arik, S. and Orman, Z., Global stability analysis of Cohen-Grossberg neural networks with time varying delays, Physics Letters A, vol. 341, (2005), 410--421.
  • Takagi, T. and Sugeno, M., Fuzzy identification of systems and its applications to modeling and control, IEEE Transactions on Systems, Man and Cybernetics, vol. 15, (1983), 116--132.
  • Hou, Y.Y., Liao, T.L. and Yan, J.J., Stability analysis of Takagi-Sugeno fuzzy cellular neural networks with time-varying delays, IEEE Transactions on Systems, Man and Cybernetics, vol. 37, (2007), 720--726.
  • Yamamoto, H. and Furuhashi, T., A new sufficient condition for stable fuzzy control system and its design method, IEEE Transactions on Fuzzy Systems, vol. 9, (2001), 554--569.
  • Huang, H., Ho, D.W.C. and Lam, J., Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays, IEEE Transactions on Circuits Systems-I, Fundamental Theory and Applications,vol. 52, (2005), 251--255.
  • Bao, H., Existence and exponential stability of periodic solution for BAM fuzzy Cohen-Grossberg neural networks with mixed delays, Neural Processing Letters, vol. 43, (2016), 871--885.
  • Zheng, C. D., Zhang, X. and Wang, Z., Mode and delay-dependent stochastic stability conditions of fuzzy neural networks with Markovian jump parameters, Neural Processing Letters, vol. 43, (2016), 195--217.
  • Yang, W., Periodic solution for fuzzy Cohen-Grossberg BAM neural networks with both time-varying and distributed delays and variable coefficients, Neural Processing Letters, vol. 40, (2014), 51--73.
  • Gan, Q., Exponential synchronization of stochastic fuzzy cellular neural networks with reaction-diffusion terms via periodically intermittent control, Neural Processing Letters, vol. 37, (2013), 393--410.
  • Chandran, R. and Balasubramaniam, P., Delay dependent exponential stability for fuzzy recurrent neural networks with interval time-varying delay, Neural Processing Letters, vol. 37, (2013), 147--161.
  • Tseng, K.H, Tsai, J. S. and Lu, C. Y., Design of delay-dependent exponential estimator for T-S Fuzzy Neural networks with mixed time-varying interval delays using hybrid Taguchi-Genetic algorithm, Neural Processing Letters, vol. 36, (2012), 49--67.
  • Ahn, C. K., Takagi-Sugeno fuzzy Hopfield neural networks for H-infinity nonlinear system identification, Neural Processing Letters, vol. 34, (2011), 59--70.
  • Gan, Q., Xu, R. and Yang, P., Stability analysis of stochastic fuzzy cellular neural networks with time-varying delays and reaction-diffusion terms, Neural Processing Letters, vol. 32,( 2010), 45--57.
  • Yang, W., Yu, W., Cao, J., Alsaadi, F. E. and Hayat, T., Global exponential stability and lag synchronization for delayed memristive fuzzy Cohen-Grossberg BAM neural networks with impulses, Neural Networks, vol. 98, (2018), 122-153.
  • Jian, J. and Jiang, W., Lagrange exponential stability for fuzzy Cohen-Grossberg neural networks with time-varying delays, Fuzzy Sets and Systems, vol. 277, (2017), 65--80.
  • Muralisankar, S. and Gopalakrishnan, N., Robust stability criteria for Takagi-Sugeno fuzzy Cohen-Grossberg neural networks of neutral type, Neurocomputing, vol. 144, (2014), 516-525.
  • Li, C., Li, Y. and Ye, Y., Exponential stability of fuzzy Cohen-Grossberg neural networks with time delays and impulsive effects, Communications in Nonlinear Science and Numerical Simulation, vol. 15, (2010), 3599-3606.
  • Zhu, Q. and Li, X., Exponential and almost sure exponential stability of stochastic fuzzy delayed Cohen-Grossberg neural networks, Fuzzy Sets and Systems, vol. 203, (2012), 74-94.
  • Mathiyalagan, K., Park, J H., Sakthivel, R. and Anthoni, S. M., Delay fractioning approach to robust exponential stability of fuzzy Cohen-Grossberg neural networks, Applied Mathematics and Computation, vol.230, (2014), 451-463.
  • Bao, G., Wen, S. and Zeng, Z., Robust stability analysis of interval fuzzy Cohen-Grossberg neural networks with piecewise constant argument of generalized type , Neural Networks, vol. 33, 2012, 32--41.
  • Balasubramaniam, P. and Ali, M. S., Stability analysis of Takagi-Sugeno fuzzy Cohen-Grossberg BAM neural networks with discrete and distributed time-varying delays, Mathematical and Computer Modelling, vol. 53, (2011), 151--160.
  • Li, C., Li, Y. and Ye, Yuan, Exponential stability of fuzzy Cohen-Grossberg neural networks with time delays and impulsive effects, Communications in Nonlinear Science and Numerical Simulation, vol. 15, (2010), pp. 3599--3606.
  • He, D. and Xu, D., Attracting and invariant sets of fuzzy Cohen-Grossberg neural networks with time-varying delays, Physics Letters A, vol. 372, (2008), 7057--7062.

Year 2019, Volume: 68 Issue: 2, 1411 - 1426, 01.08.2019

Neyir Ozcan

https://doi.org/10.31801/cfsuasmas.455799
Cited By: 1

Abstract

References

  • Cohen, M.A. and Grossberg, S., Absolute stability and global pattern formation and parallel memory storage by competitive neural networks, IEEE Transactions on Systems, Man and Cybernetics, vol. 13, (1983), 815-821.
  • Li, L. and Jian, J., Exponential convergence and Lagrange stability for impulsive Cohen-Grossberg neural networks with time-varyin delays, Journal of Computational and Applied Mathematics, vol. 277, (2015), 23-35.
  • Yu, S,. Zhang, Z. and Quan, Z., New global exponential stability conditions for inertial Cohen-Grossberg neural networks with time delays, Neurocomputing, vol. 151, (2015), 1446-1454.
  • Liu, Y., Liu, W., Obaid, M. A. and Abbas, I. A., Exponential stability of Markovian jumping Cohen-Grossberg neural networks with mixed mode-dependent time-delays, Neurocomputing, vol. 177, (2016), 409-415.
  • Esteves, S. and Oliveira, J. J., Global asymptotic stability of nonautonomous Cohen-Grossberg neural network models with infinite delays, Applied Mathematics and Computation, vol. 265, (2015), 333-346.
  • Ozcan, N., New conditions for global stability of neutral-type delayed Cohen-Grossberg neural networks, Neural Networks, vol. 106, (2018), 1-7.
  • Du, Y. and Xu, R., Multistability and multiperiodicity for a class of Cohen-Grossberg BAM neural networks with discontinuous activation functions and time delays, Neural Processing Letters, vol. 42, (2015), 417--435.
  • Kao, Y., Wang, C. and Zhang, L., Delay-dependent robust exponential stability of impulsive Markovian jumping reaction-diffusion Cohen-Grossberg neural networks, Neural Processing Letters, vol. 38, (2013), 321--346.
  • Li, R., Cao, J., Alsaedi, A. and Ahmad, B., Passivity analysis of delayed reaction-diffusion Cohen-Grossberg neural networks via Hardy-Poincare inequality, Journal of the Franklin Institute, vol. 354, (2017), 3021--3038.
  • Li, B. and Song, Q., Some new results on periodic solution of Cohen-Grossberg neural network with impulses, Neurocomputing, vol. 177, (2016), 401--408.
  • Nie, X., Zheng, W. X. and Cao, J., Multistability of memristive Cohen-Grossberg neural networks with non-monotonic piecewise linear activation functions and time-varying delays , Neural Networks, vol. 71, (2015), 27--36.
  • Wei, T., Wang, L. and Wang, Y., Existence, uniqueness and stability of mild solutions to stochastic reaction-diffusion Cohen-Grossberg neural networks with delays and Wiener processes, Neurocomputing, vol. 239, (2017), 19-27.
  • Zheng, C.D., Shan, Q. H., Zhang, H. and Wang, Z., On stabilization of stochastic Cohen-Grossberg neural networks with mode-dependent mixed time-delays and Markovian switching, IEEE Transactions on Neural Networks and Learning Systems, vol. 24, (2013), 800--811.
  • Xu, C. and Zhang, Q., On antiperiodic solutions for Cohen-Grossberg shunting inhibitory neural networks with time-varying delays and impulses, Neural Computation, vol. 26, (2014), 2328--2349. Zhu, Q.X. and Cao, J.D., Robust exponential stability of Markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays, IEEE Transactions on Neural Networks and Learning Systems, vol. 21, (2010), 1314--1325.
  • Arik, S. and Orman, Z., Global stability analysis of Cohen-Grossberg neural networks with time varying delays, Physics Letters A, vol. 341, (2005), 410--421.
  • Takagi, T. and Sugeno, M., Fuzzy identification of systems and its applications to modeling and control, IEEE Transactions on Systems, Man and Cybernetics, vol. 15, (1983), 116--132.
  • Hou, Y.Y., Liao, T.L. and Yan, J.J., Stability analysis of Takagi-Sugeno fuzzy cellular neural networks with time-varying delays, IEEE Transactions on Systems, Man and Cybernetics, vol. 37, (2007), 720--726.
  • Yamamoto, H. and Furuhashi, T., A new sufficient condition for stable fuzzy control system and its design method, IEEE Transactions on Fuzzy Systems, vol. 9, (2001), 554--569.
  • Huang, H., Ho, D.W.C. and Lam, J., Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays, IEEE Transactions on Circuits Systems-I, Fundamental Theory and Applications,vol. 52, (2005), 251--255.
  • Bao, H., Existence and exponential stability of periodic solution for BAM fuzzy Cohen-Grossberg neural networks with mixed delays, Neural Processing Letters, vol. 43, (2016), 871--885.
  • Zheng, C. D., Zhang, X. and Wang, Z., Mode and delay-dependent stochastic stability conditions of fuzzy neural networks with Markovian jump parameters, Neural Processing Letters, vol. 43, (2016), 195--217.
  • Yang, W., Periodic solution for fuzzy Cohen-Grossberg BAM neural networks with both time-varying and distributed delays and variable coefficients, Neural Processing Letters, vol. 40, (2014), 51--73.
  • Gan, Q., Exponential synchronization of stochastic fuzzy cellular neural networks with reaction-diffusion terms via periodically intermittent control, Neural Processing Letters, vol. 37, (2013), 393--410.
  • Chandran, R. and Balasubramaniam, P., Delay dependent exponential stability for fuzzy recurrent neural networks with interval time-varying delay, Neural Processing Letters, vol. 37, (2013), 147--161.
  • Tseng, K.H, Tsai, J. S. and Lu, C. Y., Design of delay-dependent exponential estimator for T-S Fuzzy Neural networks with mixed time-varying interval delays using hybrid Taguchi-Genetic algorithm, Neural Processing Letters, vol. 36, (2012), 49--67.
  • Ahn, C. K., Takagi-Sugeno fuzzy Hopfield neural networks for H-infinity nonlinear system identification, Neural Processing Letters, vol. 34, (2011), 59--70.
  • Gan, Q., Xu, R. and Yang, P., Stability analysis of stochastic fuzzy cellular neural networks with time-varying delays and reaction-diffusion terms, Neural Processing Letters, vol. 32,( 2010), 45--57.
  • Yang, W., Yu, W., Cao, J., Alsaadi, F. E. and Hayat, T., Global exponential stability and lag synchronization for delayed memristive fuzzy Cohen-Grossberg BAM neural networks with impulses, Neural Networks, vol. 98, (2018), 122-153.
  • Jian, J. and Jiang, W., Lagrange exponential stability for fuzzy Cohen-Grossberg neural networks with time-varying delays, Fuzzy Sets and Systems, vol. 277, (2017), 65--80.
  • Muralisankar, S. and Gopalakrishnan, N., Robust stability criteria for Takagi-Sugeno fuzzy Cohen-Grossberg neural networks of neutral type, Neurocomputing, vol. 144, (2014), 516-525.
  • Li, C., Li, Y. and Ye, Y., Exponential stability of fuzzy Cohen-Grossberg neural networks with time delays and impulsive effects, Communications in Nonlinear Science and Numerical Simulation, vol. 15, (2010), 3599-3606.
  • Zhu, Q. and Li, X., Exponential and almost sure exponential stability of stochastic fuzzy delayed Cohen-Grossberg neural networks, Fuzzy Sets and Systems, vol. 203, (2012), 74-94.
  • Mathiyalagan, K., Park, J H., Sakthivel, R. and Anthoni, S. M., Delay fractioning approach to robust exponential stability of fuzzy Cohen-Grossberg neural networks, Applied Mathematics and Computation, vol.230, (2014), 451-463.
  • Bao, G., Wen, S. and Zeng, Z., Robust stability analysis of interval fuzzy Cohen-Grossberg neural networks with piecewise constant argument of generalized type , Neural Networks, vol. 33, 2012, 32--41.
  • Balasubramaniam, P. and Ali, M. S., Stability analysis of Takagi-Sugeno fuzzy Cohen-Grossberg BAM neural networks with discrete and distributed time-varying delays, Mathematical and Computer Modelling, vol. 53, (2011), 151--160.
  • Li, C., Li, Y. and Ye, Yuan, Exponential stability of fuzzy Cohen-Grossberg neural networks with time delays and impulsive effects, Communications in Nonlinear Science and Numerical Simulation, vol. 15, (2010), pp. 3599--3606.
  • He, D. and Xu, D., Attracting and invariant sets of fuzzy Cohen-Grossberg neural networks with time-varying delays, Physics Letters A, vol. 372, (2008), 7057--7062.
There are 37 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Review Articles
Authors

Neyir Ozcan 0000-0002-5513-9072

Publication Date August 1, 2019
Submission Date August 29, 2018
Acceptance Date February 14, 2019
Published in Issue Year 2019 Volume: 68 Issue: 2

Cite

APA Ozcan, N. (2019). Equilibrium and Stability Analysis of Takagi-Sugeno Fuzzy Delayed Cohen-Grossberg Neural Networks. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1411-1426. https://doi.org/10.31801/cfsuasmas.455799
AMA Ozcan N. Equilibrium and Stability Analysis of Takagi-Sugeno Fuzzy Delayed Cohen-Grossberg Neural Networks. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):1411-1426. doi:10.31801/cfsuasmas.455799
Chicago Ozcan, Neyir. “Equilibrium and Stability Analysis of Takagi-Sugeno Fuzzy Delayed Cohen-Grossberg Neural Networks”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 1411-26. https://doi.org/10.31801/cfsuasmas.455799.
EndNote Ozcan N (August 1, 2019) Equilibrium and Stability Analysis of Takagi-Sugeno Fuzzy Delayed Cohen-Grossberg Neural Networks. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1411–1426.
IEEE N. Ozcan, “Equilibrium and Stability Analysis of Takagi-Sugeno Fuzzy Delayed Cohen-Grossberg Neural Networks”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1411–1426, 2019, doi: 10.31801/cfsuasmas.455799.
ISNAD Ozcan, Neyir. “Equilibrium and Stability Analysis of Takagi-Sugeno Fuzzy Delayed Cohen-Grossberg Neural Networks”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 1411-1426. https://doi.org/10.31801/cfsuasmas.455799.
JAMA Ozcan N. Equilibrium and Stability Analysis of Takagi-Sugeno Fuzzy Delayed Cohen-Grossberg Neural Networks. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1411–1426.
MLA Ozcan, Neyir. “Equilibrium and Stability Analysis of Takagi-Sugeno Fuzzy Delayed Cohen-Grossberg Neural Networks”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 1411-26, doi:10.31801/cfsuasmas.455799.
Vancouver Ozcan N. Equilibrium and Stability Analysis of Takagi-Sugeno Fuzzy Delayed Cohen-Grossberg Neural Networks. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1411-26.

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