New Delay-Dependent Stability Criteria for Neural Networks With Two Additive Time-varying Delay Components

In this paper, the problem of stability criteria of neural networks (NNs) with two-additive time-varying delay compenents is investigated. The relationship between the time-varying delay and its lower and upper bounds is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some improved delay stability criteria for NNs with two-additive time-varying delay components are proposed. Finally, a numerical example is given to illustrate the effectiveness of the proposed method. Keywords—Delay-dependent stability; Time-varying delays; Lyapunov functional; Linear matrix inequality(LMI).

[1]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[2]  Lihua Xie,et al.  Output feedback H∞ control of systems with parameter uncertainty , 1996 .

[3]  S. Arik,et al.  On the global asymptotic stability of delayed cellular neural networks , 2000 .

[4]  Teh-Lu Liao,et al.  Global stability for cellular neural networks with time delay , 2000, IEEE Trans. Neural Networks Learn. Syst..

[5]  Sabri Arik,et al.  An analysis of global asymptotic stability of delayed cellular neural networks , 2002, IEEE Trans. Neural Networks.

[6]  Jinde Cao,et al.  Exponential stability and periodic oscillatory solution in BAM networks with delays , 2002, IEEE Trans. Neural Networks.

[7]  Tianping Chen,et al.  Delay-independent stability analysis of Cohen-Grossberg neural networks , 2003 .

[8]  S. Arik.  Global asymptotic stability of a larger class of neural networks with constant time delay , 2003 .

[9]  Vimal Singh,et al.  A generalized LMI-based approach to the global asymptotic stability of delayed cellular neural networks , 2004, IEEE Transactions on Neural Networks.

[10]  Sabri Arik,et al.  An analysis of exponential stability of delayed neural networks with time varying delays , 2004, Neural Networks.

[11]  Vimal Singh,et al.  Global robust stability of delayed neural networks: an LMI approach , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

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

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

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

[15]  Yu Zhao,et al.  Asymptotic stability analysis of neural networks with successive time delay components , 2008, Neurocomputing.

[16]  Hongyi Li,et al.  Robust exponential stability for uncertain stochastic neural networks with discrete and distributed time-varying delays☆ , 2008 .

[17]  Xun-lin Zhu,et al.  Delay-dependent exponential stability for neural networks with discrete and distributed time-varying delays , 2009 .

[18]  Zidong Wang,et al.  Global synchronization for delayed complex networks with randomly occurring nonlinearities and multiple stochastic disturbances , 2009 .

[19]  Feipeng Da,et al.  Mean-square exponential stability of stochastic Hopfield neural networks with time-varying discrete and distributed delays , 2009 .

[20]  Xiangbing Zhou,et al.  Improved asymptotic stability criteria for neural networks with interval time-varying delay , 2010, Expert Syst. Appl..

[21]  Xiangjun Xie,et al.  New asymptotic stability criteria for neural networks with time-varying delay , 2010 .

[22]  Zidong Wang,et al.  Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays , 2010, IEEE Transactions on Neural Networks.

[23]  Zidong Wang,et al.  On Robust Stability of Stochastic Genetic Regulatory Networks With Time Delays: A Delay Fractioning Approach , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[24]  Zidong Wang,et al.  Exponential Stabilization of a Class of Stochastic System With Markovian Jump Parameters and Mode-Dependent Mixed Time-Delays , 2010, IEEE Transactions on Automatic Control.

[25]  Pagavathigounder Balasubramaniam,et al.  Stability analysis of Takagi-Sugeno fuzzy Cohen-Grossberg BAM neural networks with discrete and distributed time-varying delays , 2011, Math. Comput. Model..

[26]  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.