Robust Stability of Uncertain Neural Networks with Time-Varying Delays

This paper is concerned the robust stability analysis problem for neural networks with time-varying delay and time-varying parametric uncertainties. By utilizing a Lyapunov-Krasovskii functional, we show that the addressed neural networks are robustly, asymptotically stable if a convex optimization problem is feasible. A stability criterion is derived and formulated by means of the feasibility of a linear matrix inequality (LMI), which can be effectively solved by some standard numerical packages. Two numerical examples are given to demonstrate the usefulness of the proposed robust stability criterion.

[1]  Qing-Chang Zhong,et al.  Robust stability analysis of simple systems controlled over communication networks , 2003, Autom..

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

[3]  J. Yan,et al.  A new result on the robust stability of uncertain systems with time-varying delay , 2001 .

[4]  Vladimir A. Yakubovich,et al.  Linear Matrix Inequalities in System and Control Theory (S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan) , 1995, SIAM Rev..

[5]  Bugong Xu,et al.  Delay-independent stability criteria for linear continuous systems with time-varying delays , 2002, Int. J. Syst. Sci..

[6]  Guanrong Chen,et al.  LMI-based approach for asymptotically stability analysis of delayed neural networks , 2002 .

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

[8]  Te-Jen Su,et al.  Robust stability of interval time-delay systems with delay-dependence , 1998 .

[9]  Xiaofeng Liao,et al.  LMI-based robust stability analysis of neural networks with time-varying delay , 2005, Neurocomputing.

[10]  K. Mizukami,et al.  Robust stability criteria for dynamical systems including delayed perturbations , 1995, IEEE Trans. Autom. Control..

[11]  Vimal Singh,et al.  LMI approach to the global robust stability of a larger class of neural networks with delay , 2007 .

[12]  Chuandong Li,et al.  An LMI approach to asymptotical stability of multi-delayed neural networks , 2005 .

[13]  Yuechao Wang,et al.  An LMI approach to stability of systems with severe time-delay , 2004, IEEE Transactions on Automatic Control.

[14]  Jinde Cao,et al.  Global asymptotic stability of neural networks with transmission delays , 2000, Int. J. Syst. Sci..

[15]  S. Arik.  Global robust stability of delayed neural networks , 2003 .

[16]  V. Singh.  Robust stability of cellular neural networks with delay: linear matrix inequality approach , 2004 .

[17]  Guanrong Chen,et al.  Novel robust stability criteria for interval-delayed Hopfield neural networks , 2001 .