Title: New delay-dependent exponential stability for discrete-time recurrent neural networks with mixed time-delays

Authors: Cheng-De Zheng; Chao-Ke Gong; Zhanshan Wang

Addresses: School of Science, Dalian Jiaotong University, Dalian, 116028, China ' School of Science, Dalian Jiaotong University, Dalian, 116028, China ' School of Information Science and Engineering, Northeastern University, Shenyang, 110004, China

Abstract: The existence, uniqueness and globally exponential stability is investigated for a class of discrete-time recurrent neural networks with discrete and bounded distributed delays. The activation functions are required to be neither bounded nor monotonic. By introducing triple-sum terms, a new Lyapunov-Krasovskii functional is constructed. After using the homeomorphism mapping principle, discrete Jensen inequality and generalised discrete Jensen inequality, a linear matrix inequality (LMI) approach is developed to establish delay-dependent sufficient conditions for exponential stability of the discrete-time neural networks. As the obtained conditions are expressed in terms of LMIs, the feasibility can be easily checked by using the numerically efficient MATLAB LMI toolbox. Two numerical examples are also given to show the effectiveness of our results.

Keywords: global exponential stability; discrete-time neural networks; linear matrix inequality; LMI; mixed time delays; free-weighting matrix; homeomorphism mapping.

DOI: 10.1504/IJICA.2013.053173

International Journal of Innovative Computing and Applications, 2013 Vol.5 No.2, pp.65 - 75

Received: 06 Jul 2011
Accepted: 06 Nov 2011

Published online: 31 Jul 2014 *

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