Delay-Dependent Exponential Stability of Cellular Neural Networks with Multi-Proportional Delays

Global exponential stability of a class of cellular neural networks with multi-proportional delays is investigated. New delay-dependent sufficient conditions ensuring global exponential stability for the system presented here are related to the size of the proportional delay factor, by employing matrix theory and Lyapunov functional, and without assuming the differentiability, boundedness and monotonicity of the activation functions. Two examples and their simulation results are given to illustrate the effectiveness of the obtained results.

[1]  Jinde Cao,et al.  Almost sure exponential stability of stochastic cellular neural networks with unbounded distributed delays , 2009, Neurocomputing.

[2]  Zhou Li-qun Exponential Stability of a Class of Cellular Neural Networks with Multi-Pantograph Delays , 2012 .

[3]  Arieh Iserles,et al.  The asymptotic behaviour of certain difference equations with proportional delays , 1994 .

[4]  Yunkang Liu,et al.  Asymptotic behaviour of functional-differential equations with proportional time delays , 1996, European Journal of Applied Mathematics.

[5]  Lu Yan,et al.  Guaranteed Cost Stabilization of Time-varying Delay Cellular Neural Networks via Riccati Inequality Approach , 2011, Neural Processing Letters.

[6]  J. B. McLeod,et al.  The functional-differential equation $y'\left( x \right) = ay\left( {\lambda x} \right) + by\left( x \right)$ , 1971 .

[7]  Yonggui Kao,et al.  Delay-dependent robust exponential stability of Markovian jumping reaction-diffusion Cohen-Grossberg neural networks with mixed delays , 2012, J. Frankl. Inst..

[8]  James Lam,et al.  Stability and Dissipativity Analysis of Distributed Delay Cellular Neural Networks , 2011, IEEE Transactions on Neural Networks.

[9]  Arieh Iserles,et al.  On Neutral Functional)Differential Equations with Proportional Delays , 1997 .

[10]  Pagavathigounder Balasubramaniam,et al.  Global asymptotic stability of BAM fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays , 2011, Math. Comput. Model..

[11]  Hanlin He,et al.  Guaranteed Cost Synchronization of Chaotic Cellular Neural Networks with Time-Varying Delay , 2012, Neural Computation.

[12]  Liping Li,et al.  Equilibrium Analysis for Improved Signal Range Model of Delayed Cellular Neural Networks , 2010, Neural Processing Letters.

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

[14]  Tan Man-chun Feedback Stabilization of Linear Systems with Proportional Delay , 2006 .

[15]  Pagavathigounder Balasubramaniam,et al.  Global asymptotic stability of stochastic fuzzy cellular neural networks with multiple time-varying delays , 2010, Expert Syst. Appl..

[16]  Wei Xing Zheng,et al.  Novel stability of cellular neural networks with interval time-varying delay , 2008, Neural Networks.

[17]  Pagavathigounder Balasubramaniam,et al.  Leakage Delays in T–S Fuzzy Cellular Neural Networks , 2011, Neural Processing Letters.

[18]  Elmar Eder,et al.  The functional differential equation x′(t) = x(x(t)) , 1984 .

[19]  Guangda Hu,et al.  Global exponential periodicity and stability of cellular neural networks with variable and distributed delays , 2008, Appl. Math. Comput..

[20]  Graeme C. Wake,et al.  Holomorphic solutions to pantograph type equations with neutral fixed points , 2004 .

[21]  Manchun Tan,et al.  Global Asymptotic Stability of Fuzzy Cellular Neural Networks with Unbounded Distributed Delays , 2010, Neural Processing Letters.

[22]  J. P. Lasalle The stability of dynamical systems , 1976 .

[23]  L. Fox,et al.  On a Functional Differential Equation , 1971 .

[24]  Jin Xu,et al.  On global exponential stability of delayed cellular neural networks with time-varying delays , 2005, Appl. Math. Comput..

[25]  Qintao Gan,et al.  Stability Analysis of Stochastic Fuzzy Cellular Neural Networks With Time-Varying Delays and Reaction-Diffusion Terms , 2010, Neural Processing Letters.

[26]  Zhigang Zeng,et al.  Global asymptotic stability and global exponential stability of delayed cellular neural networks , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[27]  Y. Liu,et al.  Global Asymptotic Stability of Stochastic Fuzzy Cellular Neural Networks with Time-Varying Delays , 2010 .

[28]  Liqun Zhou,et al.  On the Global Dissipativity of a Class of Cellular Neural Networks with Multipantograph Delays , 2011, Adv. Artif. Neural Syst..

[29]  Vimal Singh,et al.  On global exponential stability of delayed cellular neural networks , 2007 .

[30]  Guowei Yang,et al.  Exponential stability of impulsive stochastic fuzzy reaction-diffusion Cohen-Grossberg neural networks with mixed delays , 2012, Neurocomputing.

[31]  Yonggui Kao,et al.  Global exponential stability analysis for cellular neural networks with variable coefficients and delays , 2008, Neural Computing and Applications.

[32]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[33]  Leon O. Chua,et al.  Cellular neural networks with non-linear and delay-type template elements and non-uniform grids , 1992, Int. J. Circuit Theory Appl..