Direct delay decomposition approach to synchronization of chaotic fuzzy cellular neural networks with discrete, unbounded distributed delays and Markovian jumping parameters

In this paper, the problem of synchronization of chaotic fuzzy cellular neural networks (FCNNs) with discrete, unbounded distributed delays and Markovian jumping parameters (MJPs) is investigated. Sufficient delay-dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs) to ensure the chaotic delayed FCNNs to be stochastic asymptotically synchronous with the help of free-weighting matrix and some inequality techniques. The information of the delayed plant states can be taken into full consideration. Here, the delay interval is decomposed into two subintervals by using the tuning parameter ? such that 0 < ? < 1 . By developing a delay decomposition approach and constructing suitable Lyapunov-Krasovskii functional (LKF), sufficient conditions for synchronization are established for each subinterval. Numerical example and its simulations are provided to demonstrate the effectiveness and less conservatism of the derived results.

[1]  Ta-lun Yang,et al.  The global stability of fuzzy cellular neural network , 1996 .

[2]  Ke Jing.  Exponential stability of FCNNs with time-varying leakage delays and reaction-diffusion terms , 2014, Neurocomputing.

[3]  Qing Zhu,et al.  Design of exponential state estimator for neural networks with distributed delays , 2009 .

[4]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[5]  K. Gu,et al.  Stability of Linear Systems With Time‐Varying Delay: a Generalized Discretized Lyapunov Functional Approach , 2001 .

[6]  Xiaomei Feng,et al.  Global exponential synchronization of delayed fuzzy cellular neural networks with impulsive effects , 2011 .

[7]  Rui Xu,et al.  Exponential synchronization of stochastic fuzzy cellular neural networks with time delay in the leakage term and reaction–diffusion , 2012 .

[8]  Rathinasamy Sakthivel,et al.  Robust stability criteria for discrete-time switched neural networks with various activation functions , 2012, Appl. Math. Comput..

[9]  Lin-Bao Yang,et al.  Cellular neural networks: theory , 1988 .

[10]  Ju H. Park,et al.  Extended Dissipative Analysis for Neural Networks With Time-Varying Delays , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[11]  Zhidong Teng,et al.  Exponential lag synchronization for delayed fuzzy cellular neural networks via periodically intermittent control , 2012, Math. Comput. Simul..

[12]  Qintao Gan,et al.  Exponential Synchronization of Stochastic Fuzzy Cellular Neural Networks with Reaction-Diffusion Terms via Periodically Intermittent Control , 2012, Neural Processing Letters.

[13]  Yang Tang,et al.  Robust synchronization in an array of fuzzy delayed cellular neural networks with stochastically hybrid coupling , 2009, Neurocomputing.

[14]  Leon O. Chua,et al.  Cellular neural networks: applications , 1988 .

[15]  Wei Zhang,et al.  Chaotic synchronization and secure communication based on descriptor observer , 2009 .

[16]  Ju H. Park,et al.  Passivity-based control for Hopfield neural networks using convex representation , 2011, Appl. Math. Comput..

[17]  Alexey A. Koronovskii,et al.  Generalized synchronization of chaos for secure communication: Remarkable stability to noise , 2010, 1302.4067.

[18]  Xuyang Lou,et al.  Robust asymptotic stability of uncertain fuzzy BAM neural networks with time-varying delays , 2007, Fuzzy Sets Syst..

[19]  Ping Yan,et al.  Exponential synchronization of fuzzy cellular neural networks with mixed delays and general boundary conditions , 2012 .

[20]  Pagavathigounder Balasubramaniam,et al.  Linear matrix inequality approach for synchronization control of fuzzy cellular neural networks with mixed time delays , 2012 .

[21]  Yan Liu,et al.  Global exponential stability of delayed fuzzy cellular neural networks with Markovian jumping parameters , 2011, Neural Computing and Applications.

[22]  Ju H. Park,et al.  Robust synchronisation of chaotic systems with randomly occurring uncertainties via stochastic sampled-data control , 2013, Int. J. Control.

[23]  Ju H. Park,et al.  Delay fractioning approach to robust exponential stability of fuzzy Cohen-Grossberg neural networks , 2014, Appl. Math. Comput..

[24]  S. M. Lee,et al.  Secure communication based on chaotic synchronization via interval time-varying delay feedback control , 2011 .

[25]  James J. Buckley,et al.  Stability analysis of neural net controllers using fuzzy neural networks , 1999, Fuzzy Sets Syst..

[26]  Corentin Briat,et al.  Convergence and Equivalence Results for the Jensen's Inequality—Application to Time-Delay and Sampled-Data Systems , 2011, IEEE Transactions on Automatic Control.

[27]  Petr Ekel,et al.  Improved asymptotic stability analysis for uncertain delayed state neural networks , 2009 .

[28]  Ju H. Park,et al.  Exponential synchronization criteria for Markovian jumping neural networks with time-varying delays and sampled-data control , 2014 .

[29]  Petr Ekel,et al.  Asymptotic stability analysis in uncertain multi-delayed state neural networks via Lyapunov-Krasovskii theory , 2007, Math. Comput. Model..

[30]  Rui Xu,et al.  Synchronization of non-identical chaotic delayed fuzzy cellular neural networks based on sliding mode control☆ , 2012 .

[31]  Yonggang Chen,et al.  Stability analysis for neural networks with time-varying delay: A more general delay decomposition approach , 2010, Neurocomputing.

[32]  Leon O. Chua,et al.  Fuzzy cellular neural networks: applications , 1996, 1996 Fourth IEEE International Workshop on Cellular Neural Networks and their Applications Proceedings (CNNA-96).

[33]  Petr Ekel,et al.  Novel stability criteria for uncertain delayed Cohen–Grossberg neural networks using discretized Lyapunov functional , 2009 .

[34]  Haijun Jiang,et al.  Global exponential synchronization of fuzzy cellular neural networks with delays and reaction-diffusion terms , 2011, Neurocomputing.

[35]  Louis M. Pecora,et al.  Synchronizing chaotic circuits , 1991 .

[36]  Leon O. Chua,et al.  Fuzzy cellular neural networks: theory , 1996, 1996 Fourth IEEE International Workshop on Cellular Neural Networks and their Applications Proceedings (CNNA-96).

[37]  Ju H. Park,et al.  Delay-dependent H∞ state estimation of neural networks with mixed time-varying delays , 2014, Neurocomputing.

[38]  Ju H. Park,et al.  Robust mixed H∞ and passive filtering for networked Markov jump systems with impulses , 2014, Signal Process..

[39]  Q. Gan,et al.  Synchronization of Stochastic Fuzzy Cellular Neural Networks with Leakage Delay Based on Adaptive Control , 2014 .

[40]  Guang-Hong Yang,et al.  New results of stability analysis for systems with time‐varying delay , 2010 .