Stability and Dissipativity Analysis for Neutral Type Stochastic Markovian Jump Static Neural Networks with Time Delays

Open access

Abstract

This paper studies the global asymptotic stability and dissipativity problem for a class of neutral type stochastic Markovian Jump Static Neural Networks (NTSMJSNNs) with time-varying delays. By constructing an appropriate Lyapunov-Krasovskii Functional (LKF) with some augmented delay-dependent terms and by using integral inequalities to bound the derivative of the integral terms, some new sufficient conditions have been obtained, which ensure that the global asymptotic stability in the mean square. The results obtained in this paper are expressed in terms of Strict Linear Matrix Inequalities (LMIs), whose feasible solutions can be verified by effective MATLAB LMI control toolbox. Finally, examples and simulations are given to show the validity and advantages of the proposed results.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] J. Liang and J. Cao A based-on LMI stability criterion for delayed recurrent neural networks” Chaos Solitons & Fractals 28 (2006) 154-160.

  • [2] O. M. Kwon J. H. Park New delay-dependent robust stability criterion for uncertain neural networks with time-varying delays Applied Mathematics and Computation 205 (2008) 417-427.

  • [3] Y. Liu S. M. Lee H. G. Lee Robust delay-depent stability criteria for uncertain neural networks with two additive time-varying delay components Neurocomputing 151 (2015) 770-775.

  • [4] H. B. Zeng J. H. Park C. F. Zhang W. Wang Stability and dissipativity analysis of static neural networks with interval time-varying delay Journal of the Franklin Institute 352 (2015) 1284-1295.

  • [5] P. Muthukumar K. Subramanian Stability criteria for Markovian jump neural networks with mode-dependent additive time-varying delays via quadratic convex combination Neurocomputing 205 (2016) 75-83.

  • [6] T. Wang S. Zhao W. Zhou W. Yu Finite-time state estimation for delayed Hopfield neural networks with Markovian jump Neurocomputing 156 (2015) 193-198.

  • [7] X. Mao Stochastic Differential Equations and Applications Chichester: Horwood 1997.

  • [8] Q. Zhu J. Cao Robust exponential stability of Markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays IEEE Transactions on Neural Networks 21 (2010) 1314-1325.

  • [9] G. Chen J. Xia G. Zhuang Delay-dependent stability and dissipativity analysis of generalized neural networks with Markovian jump parameters and two delay components Journal of the Franklin Institute 353 (2016) 2137-2158.

  • [10] Q. Zhu J. Cao Exponential stability of stochastic neural networks with both Markovian jump parameters and mixed time delays IEEE Transactions on Systems Man and Cybernetics Part B 41 (2011) 341-353.

  • [11] Y. Chen W. Zheng Stability analysis of time-delay neural networks subject to stochastic perturbations IEEE Transactions on Cybernatics 43 (2013) 2122-2134.

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

  • [13] S. Zhu M. Shen C. C. Lim Robust input-to-state stability of neural networks with Markovian switching in presence of random disturbances or time delays Neurocomputing 249 (2017) 245-252.

  • [14] E. K. Boukas Z. K. Liu G. X. Liu Delay-dependent robust stability and H control of jump linear systems with time-delay International Journal of Control 74 (2001) 329-340.

  • [15] Y. Y. Cao J. Lam L. S. Hu Delay-dependent stochastic stability and H analysis for time-delay systems with Markovian jumping parameters Journal of the Franklin Institute 340 (2003) 423-434.

  • [16] R. Samidurai R. Manivannan C. K. Ahn H. R. Karimi New criteria for stability of generalized neural networks including Markov jump parameters and additive time delays IEEE Transactions on Systems Man and Cybernetics: Systems 48 (2018) 485-499.

  • [17] S. Blythe X. Mao and X. Liao Stability of stochastic delay neural networks Journal of the Franklin Institute 338 (2001) 481-495.

  • [18] Z. Zhao Q. Song S. He Passivity analysis of stochastic neural networks with time-varying delays and leakage delay Neurocomputing 125 (2014) 22-27.

  • [19] C. Wang Y. Shen Delay-dependent non-fragile robust stabilization and H control of uncertain stochastic systems with time-varying delay and non-linearity Journal of the Franklin Institute 348 (2011) 2174-2190.

  • [20] G. Liu S. X. Yang Y. Chai W. Feng W. Fu Robust stability criteria for uncertain stochastic neural networks of neutral-type with interval time-varying delays Neural Computing and Applications 22 (2013) 349-359.

  • [21] R. Yang H. Gao P. Shi Novel robust stability criteria for stochastic Hopfield neural networks with time delays IEEE Transactions on Systems Man and Cybernetics Part B 39 (2009) 467-474.

  • [22] Q. Song Z. Wang Stability analysis of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays Physica A: Statistical Mechanics and its Applications 387 (2008) 3314-3326.

  • [23] S. Zhu Y. Shen Passivity analysis of stochastic delayed neural networks with Markovian switching Neurocomputing 74 (2011) 1754-1761.

  • [24] L. Pan J. Cao Robust stability for uncertain stochastic neural network with delay and impulses Neurocomputing 94 (2012) 102-110.

  • [25] R. Samidurai R. Manivannan Delay-rangedependent passivity analysis for uncertain stochastic neural networks with discrete and distributed time-varying delays Neurocomputing 185 (2016) 191-201.

  • [26] Q. Song J. Liang Z. Wang Passivity analysis of discrete-time stochastic neural networks with time-varying delays Neurocomputing 72 (2009) 1782-1788.

  • [27] S. Zhu Y. Shen Robustness analysis for connection weight matrices of global exponential stability of stochastic recurrent neural networks Neural Networks 38 (2013) 17-22.

  • [28] C. Cheng T. Liao J. Yan C. Hwang Globally asymptotic stability of a class of neutral-type neural networks with delays IEEE Transactions on Systems Man and CyberneticsPart B 36 (2006) 1191-1195.

  • [29] R. Samidurai S. Rajavel Q. Zhu R. Raja H. Zhou Robust passivity analysis for neutral-type neural networks with mixed and leakage delays Neurocomputing 175 (2016) 635-643.

  • [30] Z. Tu J. Cao A. Alsaedi F. Alsaadi Global dissipativity of memristor-based neutral type inertial neural networks Neural Networks 88 (2017) 125-133.

  • [31] R. Samidurai S. Rajavel R. Sriraman J. Cao A. Alsaedi F. E Alsaadi Novel results on stability analysis of neutral-type neural networks with additive time-varying delay components and leakage delay International Journal of Control Automation and Systems 15 (2016) 1888-1900.

  • [32] R. Manivannan R. Samidurai J. Cao A. Alsaedi F. E. Alsaadi Stability analysis of interval time-varying delayed neural networks including neutral time-delay and leakage delay Chaos Solitons & Fractals 114 (2018) 433-445.

  • [33] K. Mathiyalagan R. Sakthivel and S. Marshal Anthoni Robust exponential stability and H control for switched neutral-type neural networks International Journal of Adaptive Control and Signal Processing 28 (2014) 429-443.

  • [34] R. Sakthivel R. Anbuvithya K. Mathiyalagan A. Arunkumar and P. Prakash New LMI-based passivity criteria for neutral-type BAM neural networks with randomly occurring uncertainties Reports on Mathematical Physics 72 (2013) 263-286.

  • [35] J. C. Willems Dissipative dynamical systems part I: General theory Archive for Rational Mechanics and Analysis 45 (1972) 321-351.

  • [36] D. L. Hill P. J. Moylan Dissipative dynamical systems: basic input-output and state properties Journal of the Franklin Institute 309 (1980) 327-357.

  • [37] G. Nagamani S. Ramasamy Stochastic dissipativity and passivity analysis for discrete-time neural networks with probabilistic time-varying delays in the leakage term Applied Mathematics and Computation 289 (2016) 237-257.

  • [38] Z. G. Wu Ju. H. Park H. Su and J. Chu Robust dissipativity analysis of neural networks with time-varying delay and randomly occurring uncertainties Nonlinear Dynamics 69 (2012) 1323-1332.

  • [39] Z. Feng and J. Lam Stability and dissipativity analysis of distributed delay cellular neural networks IEEE Transactions on Neural Networks 22 (2011) 976-981.

  • [40] R. Raja U. K. Raja R. Samidurai and A. Leelamani Dissipativity of discrete-time BAM stochastic neural networks with Markovian switching and impulses Journal of the Franklin Institute 350 (2013) 3217-3247.

  • [41] R. Manivannan R. Samidurai Q. Zhu Further improved results on stability and dissipativity analysis of static impulsive neural networks with interval time-varying delays Journal of the Franklin Institute 354 (2017) 6312-6340.

  • [42] Z. Zuo C. Yang and Y. Wang A new method for stability analysis of recurrent neural networks with interval time-varying delay IEEE Transactions on Neural Networks 21 (2010) 339-344.

  • [43] X. Li H. Gao and X. Yu A unified approach to the stability of generalized static neural networks with linear fractional IEEE Transactions Systems Man Cybernetics. Part B 41 (2011) 1275-1286.

  • [44] Y. Q. Bai and J. Chen New stability criteria for recurrent neural networks with interval time-varying delay Neurocomputing 121 (2013) 179-184.

  • [45] X. M. Zhang and Q. L. Han Global asymptotic stability analysis for delayed neural networks using a matrix-based quadratic convex approach Neural Networks 54 (2014) 57-69.

  • [46] H. D. Choi C. K. Ahn M. T. Lim M. K. Song Dynamic output-feedback H control for active half-vehicle suspension systems with time-varying input delay International Journal of Control Automation and Systems 14 (2016) 59-68.

  • [47] P. G. Park S. Y. Lee W. I. Lee Auxiliary function-based integral inequalities for quadratic functions and their applications to time delay systems Journal of the Franklin Institute 352 (2015) 1378-1396.

  • [48] P. G. Park J. W. Ko C. Jeong Reciprocally convex approach to stability of systems with time-varying delays Automatica 47 (2011) 235-238.

Search
Journal information
Impact Factor


CiteScore 2018: 4.70

SCImago Journal Rank (SJR) 2018: 0.351
Source Normalized Impact per Paper (SNIP) 2018: 4.066

Metrics
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 338 338 44
PDF Downloads 177 177 12