Global asymptotic stability of cellular neural networks with proportional delays

Proportional delay, which is different from distributed delay, is a kind of unbounded delay. The proportional delay system as an important mathematical model often rises in some fields such as physics, biology systems, and control theory. In this paper, the uniqueness and the global asymptotic stability of equilibrium point of cellular neural networks with proportional delays are analyzed. By using matrix theory and constructing suitable Lyapunov functional, delay-dependent and delay-independent sufficient conditions are obtained for the global asymptotic stability of cellular neural networks with proportional delays. These results extend previous works on these issues for the delayed cellular neural networks. Two numerical examples and their simulation are given to illustrate the effectiveness of obtained results.

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

[2]  John Ockendon,et al.  The dynamics of a current collection system for an electric locomotive , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[3]  Ewing L. Lusk,et al.  Experiments with resolution-based theorem-proving algorithms , 1982 .

[4]  G. Derfel,et al.  Kato Problem for Functional-Differential Equations and Difference Schrödinger Operators , 1990 .

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

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

[7]  Parameswaran Ramanathan,et al.  A case for relative differentiated services and the proportional differentiation model , 1999, IEEE Netw..

[8]  David K. Y. Yau,et al.  Adaptive proportional delay differentiated services: characterization and performance evaluation , 2001, TNET.

[9]  Kwong-Sak Leung,et al.  Convergence analysis of cellular neural networks with unbounded delay , 2001 .

[10]  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.

[11]  Lihong Huang,et al.  Periodic oscillation for a class of neural networks with variable coefficients , 2005 .

[12]  Cheng-Zhong Xu,et al.  A robust packet scheduling algorithm for proportional delay differentiation services , 2004, IEEE Global Telecommunications Conference, 2004. GLOBECOM '04..

[13]  Min Wu,et al.  An improved global asymptotic stability criterion for delayed cellular neural networks , 2006, IEEE Transactions on Neural Networks.

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

[15]  Zhanshan Wang,et al.  Global Asymptotic Stability of Delayed Cellular Neural Networks , 2007, IEEE Transactions on Neural Networks.

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

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

[18]  Wei Xing Zheng,et al.  Global Exponential Stability of Impulsive Neural Networks With Variable Delay: An LMI Approach , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[19]  Wen-an Zhang,et al.  Global exponential stability of cellular neural networks with time-varying discrete and distributed delays , 2009, Neurocomputing.

[20]  Ting Wang,et al.  Delay-Derivative-Dependent Stability for Delayed Neural Networks With Unbound Distributed Delay , 2010, IEEE Transactions on Neural Networks.

[21]  Wei Xing Zheng,et al.  A New Method for Complete Stability Analysis of Cellular Neural Networks With Time Delay , 2010, IEEE Transactions on Neural Networks.

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

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

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

[25]  Neyir Ozcan,et al.  A New Sufficient Condition for Global Robust Stability of Delayed Neural Networks , 2011, Neural Processing Letters.

[26]  Ping Xiong,et al.  Guaranteed cost synchronous control of time-varying delay cellular neural networks , 2011, Neural Computing and Applications.

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

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

[29]  Liqun Zhou,et al.  Delay-Dependent Exponential Stability of Cellular Neural Networks with Multi-Proportional Delays , 2012, Neural Processing Letters.

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

[31]  Yonggui Kao,et al.  Delay-Dependent Robust Exponential Stability of Impulsive Markovian Jumping Reaction-Diffusion Cohen-Grossberg Neural Networks , 2012, Neural Processing Letters.

[32]  Liqun Zhou.  Dissipativity of a class of cellular neural networks with proportional delays , 2013 .