New delay-dependent exponential stability for discrete-time recurrent neural networks with mixed time-delays. (1st January 2013)

• Record Type: Journal Article
• Authors: Zheng, Cheng-De; Gong, Chao-Ke; Wang, Zhanshan
• Is Part Of: International journal of innovative computing and applications. Volume 5:Number 2(2013)
• Page Start: 65
• Page End: 75
• Publication Date: 2013-01-01
• Subjects: global exponential stability -- discrete-time neural networks -- linear matrix inequality -- LMI -- mixed time-delays -- free-weighting matrix -- homeomorphism mapping; Evolutionary computation -- Periodicals; Neural networks (Computer science) -- Periodicals; Genetic programming (Computer science) -- Periodicals; Biologically-inspired computing -- Periodicals; Swarm intelligence -- Periodicals; Quantum computers -- Periodicals; 006.3
• Languages: English
• ISSNs: 1751-648X

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.