Novel stability criteria for uncertain delayed Cohen–Grossberg neural networks using discretized Lyapunov functional

This paper deals with the stability analysis of delayed uncertain Cohen–Grossberg neural networks (CGNN). The proposed methodology consists in obtaining new robust stability criteria formulated as linear matrix inequalities (LMIs) via the Lyapunov–Krasovskii theory. Particularly one stability criterion is derived from the selection of a parameter-dependent Lyapunov–Krasovskii functional, which allied with the Gu’s discretization technique and a simple strategy that decouples the system matrices from the functional matrices, assures a less conservative stability condition. Two computer simulations are presented to support the improved theoretical results.

[1]  Petr Ekel,et al.  Improved asymptotic stability analysis for uncertain delayed state neural networks , 2009 .

[2]  Jinde Cao,et al.  An estimation of upperbound of delays for global asymptotic stability of delayed Hopfield neural networks , 2002 .

[3]  Xiaolin Li,et al.  Stability and Bifurcation in a Neural Network Model with Two Delays , 2011 .

[4]  Stephen Grossberg,et al.  Absolute stability of global pattern formation and parallel memory storage by competitive neural networks , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[5]  Weili Xiong,et al.  Some criteria for robust stability of Cohen-Grossberg neural networks with delays , 2008 .

[6]  K. Gu.  Discretized LMI set in the stability problem of linear uncertain time-delay systems , 1997 .

[7]  Wei Wu,et al.  Some criteria for asymptotic stability of Cohen-Grossberg neural networks with time-varying delays , 2007, Neurocomputing.

[8]  Y. Chen.  Global asymptotic stability of delayed Cohen-Grossberg neural networks , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[9]  Shengyuan Xu,et al.  Relaxed Stability Conditions for Delayed Recurrent Neural Networks with Polytopic Uncertainties , 2006, Int. J. Neural Syst..

[10]  Libin Rong.  LMI-based criteria for robust stability of Cohen–Grossberg neural networks with delay , 2005 .

[11]  Zhang Chen,et al.  Dynamic analysis of high-order Cohen–Grossberg neural networks with time delay , 2007 .

[12]  Wang,et al.  Global stability and local stability of Hopfield neural networks with delays. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  Shengyuan Xu,et al.  Novel global asymptotic stability criteria for delayed cellular neural networks , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[14]  M. C. D. Oliveiraa,et al.  A new discrete-time robust stability condition ( , 1999 .

[15]  Petr Ekel,et al.  Asymptotic stability analysis in uncertain multi-delayed state neural networks via Lyapunov-Krasovskii theory , 2007, Math. Comput. Model..

[16]  Shengyuan Xu,et al.  A new LMI condition for delay-dependent asymptotic stability of delayed Hopfield neural networks , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[17]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[18]  Chuandong Li,et al.  Stability of Cohen-Grossberg neural networks with unbounded distributed delays , 2007 .

[19]  Qiang Zhang,et al.  Delay-dependent exponential stability of cellular neural networks with time-varying delays , 2005 .

[20]  Amir F. Atiya,et al.  How delays affect neural dynamics and learning , 1994, IEEE Trans. Neural Networks.

[21]  R. Westervelt,et al.  Dynamics of simple electronic neural networks , 1987 .

[22]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.