Absolute exponential stability of a class of recurrent neural networks with multiple and variable delays

Authors:
Hongtao Lu;Ruiming Shen;Fu-Lai Chung
Affiliations:
Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, People's Republic of China;Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, People's Republic of China;Department of Computing, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
Venue:
Theoretical Computer Science
Year:
2005

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Abstract

In this paper, we derive some new conditions for absolute exponential stability (AEST) of a class of recurrent neural networks with multiple and variable delays. By using the Holder's inequality and the Young's inequality to estimate the derivatives of the Lyapunov functionals, we are able to establish more general results than some existing ones. The first type of conditions established involves the convex combinations of column-sum and row-sum dominance of the neural network weight matrices, while the second type involves the p-norm of the weight matrices with p ∈ [1, +∞].