Further improvement on delay-dependent robust stability criteria for neutral-type recurrent neural networks with time-varying delays.

This paper is concerned with the problem of improved delay-dependent robust stability criteria for neutral-type recurrent neural networks (NRNNs) with time-varying delays. Combining the Lyapunov-Krasovskii functional with linear matrix inequality (LMI) techniques and integral inequality approach (IIA), delay-dependent robust stability conditions for RNNs with time-varying delay, expressed in terms of quadratic forms of state and LMI, are derived. The proposed methods contain the least number of computed variables while maintaining the effectiveness of the robust stability conditions. Both theoretical and numerical comparisons have been provided to show the effectiveness and efficiency of the present method. Numerical examples are included to show that the proposed method is effective and can provide less conservative results.

[1]  Yijing Wang,et al.  Novel Delay-Dependent Exponential Stability Analysis for a Class of Delayed Neural Networks , 2006, ICIC.

[2]  Chong Lin,et al.  Passivity analysis for uncertain neural networks with discrete and distributed time-varying delays ☆ , 2009 .

[3]  Tao Li,et al.  Improved stability criteria of neural networks with time-varying delays: An augmented LKF approach , 2010, Neurocomputing.

[4]  Tao Li,et al.  Further Results on Delay-Dependent Stability Criteria of Neural Networks With Time-Varying Delays , 2008, IEEE Transactions on Neural Networks.

[5]  Huaguang Zhang,et al.  Improved Robust Stability Criteria for Delayed Cellular Neural Networks via the LMI Approach , 2010, IEEE Transactions on Circuits and Systems II: Express Briefs.

[6]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[7]  S. Muralisankar,et al.  Robust stability criteria for Takagi-Sugeno fuzzy Cohen-Grossberg neural networks of neutral type , 2014, Neurocomputing.

[8]  T. Liao,et al.  Globally exponential stability condition of a class of neural networks with time-varying delays , 2005 .

[9]  Jin-Hua She,et al.  New delay-dependent stability criteria and stabilizing method for neutral systems , 2004, IEEE Trans. Autom. Control..

[10]  Yijing Wang,et al.  A New Method for Stability Analysis of Recurrent Neural Networks With Interval Time-Varying Delay , 2010, IEEE Transactions on Neural Networks.

[11]  J. Lam,et al.  Novel global robust stability criteria for interval neural networks with multiple time-varying delays , 2005 .

[12]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[13]  Xiaofeng Liao,et al.  Global robust asymptotical stability of multi-delayed interval neural networks: an LMI approach , 2004 .

[14]  S. C. Tong,et al.  Adaptive Neural Network Decentralized Backstepping Output-Feedback Control for Nonlinear Large-Scale Systems With Time Delays , 2011, IEEE Transactions on Neural Networks.

[15]  Tao Li,et al.  Stability Criteria With Less LMI Variables for Neural Networks With Time-Varying Delay , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[16]  Guo-Ping Liu,et al.  New Delay-Dependent Stability Criteria for Neural Networks With Time-Varying Delay , 2007, IEEE Transactions on Neural Networks.

[17]  R. Rakkiyappan,et al.  Existence, uniqueness and stability analysis of recurrent neural networks with time delay in the leakage term under impulsive perturbations , 2010 .

[18]  J. Lam,et al.  Delay-dependent exponential stability for a class of neural networks with time delays , 2005 .

[19]  Yi Zhang,et al.  A self-learning call admission control scheme for CDMA cellular networks , 2005, IEEE Transactions on Neural Networks.

[20]  Long Cheng,et al.  A Neutral-Type Delayed Projection Neural Network for Solving Nonlinear Variational Inequalities , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[21]  Huaguang Zhang,et al.  Novel stability criterions of a new fuzzy cellular neural networks with time-varying delays , 2009, Neurocomputing.

[22]  Chien-Yu Lu,et al.  Stability of cellular neural networks with time-varying delay , 2003 .

[23]  C. Liao,et al.  Passivity Analysis for Uncertain Time-Varying Delayed Neural Networks with Neutral Type , 2007, Second International Conference on Innovative Computing, Informatio and Control (ICICIC 2007).

[24]  Derong Liu,et al.  Qualitative Analysis and Synthesis of Recurrent Neural Networks , 2002 .

[25]  Sabri Arik,et al.  Global stability of a class of neural networks with time-varying delay , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[26]  Chi-Chuan Hwang,et al.  Globally Asymptotic Stability of a Class of Neutral-Type Neural Networks With Delays , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[27]  Long-Yeu Chung,et al.  Global Exponential Stability for Uncertain Delayed Neural Networks of Neutral Type With Mixed Time Delays , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[28]  Shen-Ping Xiao,et al.  New Globally Asymptotic Stability Criteria for Delayed Cellular Neural Networks , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[29]  Bing Chen,et al.  Robust Stability for Uncertain Delayed Fuzzy Hopfield Neural Networks With Markovian Jumping Parameters , 2009, IEEE Trans. Syst. Man Cybern. Part B.

[30]  Qing-Long Han,et al.  New Lyapunov-Krasovskii Functionals for Global Asymptotic Stability of Delayed Neural Networks , 2009, IEEE Trans. Neural Networks.

[31]  Ju H. Park,et al.  Further results on state estimation for neural networks of neutral-type with time-varying delay , 2009, Appl. Math. Comput..

[32]  Min Wu,et al.  Stability Analysis for Neural Networks With Time-Varying Interval Delay , 2007, IEEE Transactions on Neural Networks.

[33]  Pin-Lin Liu,et al.  Improved delay-dependent stability of neutral type neural networks with distributed delays. , 2013, ISA transactions.

[34]  Fang Liu,et al.  Exponential Stability Analysis for Neural Networks With Time-Varying Delay , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[35]  Guo-Ping Liu,et al.  Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties , 2004, IEEE Transactions on Automatic Control.

[36]  X. Guan,et al.  New results on stability analysis of neural networks with time-varying delays , 2006 .

[37]  Fang Xu,et al.  Improved delay-partitioning method to stability analysis for neural networks with discrete and distributed time-varying delays , 2014, Appl. Math. Comput..

[38]  M. Syed Ali,et al.  Novel delay-dependent stability analysis of Takagi—Sugeno fuzzy uncertain neural networks with time varying delays , 2012 .

[39]  E. Feron,et al.  History of linear matrix inequalities in control theory , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[40]  Jinde Cao,et al.  Global Asymptotical Stability of Recurrent Neural Networks With Multiple Discrete Delays and Distributed Delays , 2006, IEEE Transactions on Neural Networks.

[41]  L. Chua.  Cnn: A Paradigm for Complexity , 1998 .

[42]  Hanyong Shao,et al.  Delay-Dependent Stability for Recurrent Neural Networks With Time-Varying Delays , 2008, IEEE Transactions on Neural Networks.

[43]  Xiaoou Li,et al.  Some stability properties of dynamic neural networks , 2001 .

[44]  Xin-Ping Guan,et al.  New Exponential Stability Criteria for Neural Networks With Time-Varying Delay , 2011, IEEE Transactions on Circuits and Systems II: Express Briefs.

[45]  Yongming Li,et al.  Adaptive Neural Network Output Feedback Control for Stochastic Nonlinear Systems With Unknown Dead-Zone and Unmodeled Dynamics , 2014, IEEE Transactions on Cybernetics.

[46]  Shengyuan Xu,et al.  Delay-dependent stability of neutral type neural networks with distributed delays , 2009, Neurocomputing.

[47]  Huaguang Zhang,et al.  Global Asymptotic Stability of Recurrent Neural Networks With Multiple Time-Varying Delays , 2008, IEEE Transactions on Neural Networks.

[48]  Ju H. Park,et al.  LMI optimization approach on stability for delayed neural networks of neutral-type , 2008, Appl. Math. Comput..

[49]  Wei Wu,et al.  Some criteria for asymptotic stability of Cohen-Grossberg neural networks with time-varying delays , 2007, Neurocomputing.

[50]  Yong He,et al.  Complete Delay-Decomposing Approach to Asymptotic Stability for Neural Networks With Time-Varying Delays , 2011, IEEE Transactions on Neural Networks.

[51]  Huaguang Zhang,et al.  Novel Weighting-Delay-Based Stability Criteria for Recurrent Neural Networks With Time-Varying Delay , 2010, IEEE Transactions on Neural Networks.

[52]  Pin-Lin Liu.  Improved delay-dependent robust stability criteria for recurrent neural networks with time-varying delays. , 2013, ISA transactions.

[53]  Huaguang Zhang,et al.  Robust Exponential Stability of Recurrent Neural Networks With Multiple Time-Varying Delays , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[54]  Xin-Ping Guan,et al.  New Delay-Dependent Stability Criteria for Neural Networks With Time-Varying Delay Using Delay-Decomposition Approach , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[55]  J. Cao,et al.  LMI-based criteria for globally robust stability of delayed Cohen–Grossberg neural networks , 2006 .

[56]  Pagavathigounder Balasubramaniam,et al.  Delay-dependent asymptotic stability for stochastic delayed recurrent neural networks with time varying delays , 2008, Appl. Math. Comput..