Global asymptotic stability for cellular neural networks with discrete and distributed time-varying delays

Exponential stability criterion for interval neural networks with discrete and distributed delays

“…In this paper, a novel stability condition for neural networks with discrete and distributed delays is obtained by the Lyapunov stability theory, Homomorphic mapping theory and M-matrix theory. The obtained result improves conditions in [10][11][12][13][14]18]. The sufficient criterion in this paper does not need the differentiability of the discrete delay sðtÞ.…”

“…By choosing a appropriate Lyapunov functional, using the Lyapunov stability theory, Homomorphic mapping theory and M-matrix theory, relaxing the constraint on discrete delay sðtÞ, a new stability condition is derived. In this paper, the obtained result is less conservative than previously results in [10][11][12][13][14]18]. Finally, some illustrative numerical examples are given to illustrate the effectiveness and the advantage of the proposed result.…”

“…Some terms were omitted in the process to get the stability condition by Lyapunov functional approach in [10][11][12][13][14]18]. There is no term is omitted in this paper in the process to get stability condition.…”

“…However, as pointed out in [2], it should be noted that neural networks (NNs) usually have spatial extent due to the presence of a multitude of parallel pathways with a variety of axon sizes and lengths. In recent years, neural networks (NNs) with discrete and distributed delays has attracted much attention in research [10][11][12][13][14][15]18]. Many methods have been proposed to reduce the conservatism of the stability criteria, such as model transformation method, free-weighting matrix approach, constructing novel Lyapunov functionals method, delay decomposition technique, and weighting-matrix decomposition method.…”

Robust stability of genetic regulatory networks with distributed delay

“…Therefore, it is essential to investigate the globally robust stability of such networks with uncertainties. There have been some studies on the robust stability or distributed delays analysis for neural networks (Lien and Chung 2007;Wang et al 2006;Yang and Chu 2007). In fact, the biologic networks can show robust character under perturbation (Kwok et al 2007).…”