title: Global asymptotic stability analysis for delayed neural networks using a matrix-based quadratic convex approach.
abstract: This paper is concerned with global asymptotic stability for a class of generalized neural networks with interval time-varying delays by constructing a new Lyapunov-Krasovskii functional which includes some integral terms in the form of ∫(t-h)(t)(h-t-s)(j)ẋ(T)(s)Rjẋ(s)ds(j=1,2,3). Some useful integral inequalities are established for the derivatives of those integral terms introduced in the Lyapunov-Krasovskii functional. A matrix-based quadratic convex approach is introduced to prove not only the negative definiteness of the derivative of the Lyapunov-Krasovskii functional, but also the positive definiteness of the Lyapunov-Krasovskii functional. Some novel stability criteria are formulated in two cases, respectively, where the time-varying delay is continuous uniformly bounded and where the time-varying delay is differentiable uniformly bounded with its time-derivative bounded by constant lower and upper bounds. These criteria are applicable to both static neural networks and local field neural networks. The effectiveness of the proposed method is demonstrated by two numerical examples.
authors.affiliation: Centre for Intelligent and Networked Systems, Central Queensland University, Rockhampton QLD 4702, Australia. Electronic address: x.zhang@cqu.edu.au.
authors.forename: Xian-Ming
authors.initials: XM
authors.lastname: Zhang
authors.affiliation: Centre for Intelligent and Networked Systems, Central Queensland University, Rockhampton QLD 4702, Australia. Electronic address: q.han@cqu.edu.au.
authors.forename: Qing-Long
authors.initials: QL
authors.lastname: Han
mesh_terms: D000465:Algorithms; D006801:Humans; D008962:Models, Theoretical; D016571:Neural Networks, Computer; D013997:Time Factors; D013998:Time Perception
keywords: Generalized neural networks; Global asymptotic stability; Integral inequality; Interval time-varying delay; Matrix-based quadratic convex approach