Delay-Dependent Stability Criteria for Reaction–Diffusion Neural Networks With Time-Varying Delays

This paper studies the global asymptotic stability problem of a class of reaction-diffusion neural networks with time-varying delays. To overcome the difficulty caused by the partial differential term, a novel Lyapunov-Krasovskii functional is proposed, and a partial differential equation technique together with a linear operator approach are also applied to obtain the delay-dependent stability criteria, which are less conservative than the existing results. Finally, simulation examples are given to verify and illustrate the theoretical analysis.

[1]  Zhengqiu Zhang,et al.  Global exponential stability of interval general BAM neural networks with reaction-diffusion terms and multiple time-varying delays , 2011, Neural Networks.

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

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

[4]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[5]  Jinde Cao,et al.  Delay-independent exponential stability of stochastic Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion terms , 2007 .

[6]  Jun Peng,et al.  Delay-independent stability of stochastic reaction–diffusion neural networks with Dirichlet boundary conditions , 2010, Neural Computing and Applications.

[7]  Hamid Reza Karimi,et al.  New Delay-Dependent Exponential $H_{\infty}$ Synchronization for Uncertain Neural Networks With Mixed Time Delays , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[8]  Leon O. Chua,et al.  Autonomous cellular neural networks: a unified paradigm for pattern formation and active wave propagation , 1995 .

[9]  Huaguang Zhang,et al.  An LMI Approach to Stability Analysis of Reaction–Diffusion Cohen–Grossberg Neural Networks Concerning Dirichlet Boundary Conditions and Distributed Delays , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[10]  Xinghuo Yu,et al.  A Unified Approach to the Stability of Generalized Static Neural Networks With Linear Fractional Uncertainties and Delays , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[11]  Ángel Rodríguez-Vázquez,et al.  Reaction-diffusion navigation robot control: from chemical to VLSI analogic processors , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[13]  Luigi Fortuna,et al.  Multi-template approach to realize central pattern generators for artificial locomotion control , 2002, Int. J. Circuit Theory Appl..

[14]  Shengyuan Xu,et al.  A new approach to exponential stability analysis of neural networks with time-varying delays , 2006, Neural Networks.

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

[16]  Junguo Lu Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions , 2008 .

[17]  Jinde Cao,et al.  Global exponential stability of reaction–diffusion recurrent neural networks with time-varying delays , 2003 .

[18]  Emilia Fridman,et al.  Exponential stability of linear distributed parameter systems with time-varying delays , 2009, Autom..

[19]  James Lam,et al.  A New Criterion of Delay-Dependent Asymptotic Stability for Hopfield Neural Networks With Time Delay , 2008, IEEE Transactions on Neural Networks.

[20]  Shouming Zhong,et al.  Novel Criteria on Global Robust Exponential Stability to a Class of Reaction-Diffusion Neural Networks with Delays , 2009 .

[21]  Jinde Cao,et al.  Global asymptotic stability of a general class of recurrent neural networks with time-varying delays , 2003 .

[22]  Huijun Gao,et al.  New Delay-Dependent Exponential H ∞ Synchronization for Uncertain Neural Networks With Mixed Time Delays , 2009 .

[23]  Zhidong Teng,et al.  Impulsive Control and Synchronization for Delayed Neural Networks With Reaction–Diffusion Terms , 2010, IEEE Transactions on Neural Networks.

[24]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[25]  Jinde Cao,et al.  Exponential Stability of Stochastic Neural Networks With Both Markovian Jump Parameters and Mixed Time Delays , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[26]  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.

[27]  Jun-Guo Lu,et al.  Robust Global Exponential Stability for Interval Reaction–Diffusion Hopfield Neural Networks With Distributed Delays , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[28]  Jinde Cao,et al.  Global asymptotic and robust stability of recurrent neural networks with time delays , 2005, IEEE Trans. Circuits Syst. I Regul. Pap..

[29]  K. Gu An integral inequality in the stability problem of time-delay systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[30]  Shengyuan Xu,et al.  Delay-Dependent Exponential Stability for Uncertain Stochastic Hopfield Neural Networks With Time-Varying Delays , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[31]  Zidong Wang,et al.  Stability and Synchronization of Discrete-Time Markovian Jumping Neural Networks With Mixed Mode-Dependent Time Delays , 2009, IEEE Transactions on Neural Networks.

[32]  Shengyuan Xu,et al.  A survey of linear matrix inequality techniques in stability analysis of delay systems , 2008, Int. J. Syst. Sci..

[33]  Hamid Reza Karimi,et al.  Robust Delay-Dependent $H_{\infty}$ Control of Uncertain Time-Delay Systems With Mixed Neutral, Discrete, and Distributed Time-Delays and Markovian Switching Parameters , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[34]  Qing-Long Han,et al.  New Delay-Dependent Stability Criteria for Neural Networks With Two Additive Time-Varying Delay Components , 2011, IEEE Transactions on Neural Networks.

[35]  Wei Xing Zheng,et al.  Delay-Slope-Dependent Stability Results of Recurrent Neural Networks , 2011, IEEE Transactions on Neural Networks.

[36]  Huaguang Zhang,et al.  Global Asymptotic Stability of Reaction–Diffusion Cohen–Grossberg Neural Networks With Continuously Distributed Delays , 2010, IEEE Transactions on Neural Networks.

[37]  Anthony N. Michel,et al.  A synthesis procedure for Hopfield's continuous-time associative memory , 1990 .

[38]  Z. Guan,et al.  An LMI Approach to Exponential Stability Analysis of Neural Networks with Time-Varying Delay , 2005, TENCON 2005 - 2005 IEEE Region 10 Conference.

[39]  Yurong Liu,et al.  Robust state estimation for discrete-time stochastic neural networks with probabilistic measurement delays , 2010, Neurocomputing.

[40]  Linshan Wang,et al.  Global exponential robust stability of reaction¿diffusion interval neural networks with time-varying delays , 2006 .