Asymptotic stability of delayed neural networks: A descriptor system approach

In this paper some novel approaches to the analysis of asymptotic stability of artificial neural networks with time-varying delay are presented. These approaches are based on the Lyapunov–Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) technique. Some corresponding Lyapunov–Krasovskii functionals are introduced for stability analysis of this system with use of the descriptor and “neutral-type” model transformation without producing any additional dynamics. Delay-dependent and delay-independent stability criteria are derived for this system. Conditions are given in terms of linear matrix inequalities, and for the first time refer to neutral systems with discrete and distributed delays. The proposed criteria are less conservative than other existing criteria since they are based on an equivalent model transformation and they require bounds for fewer terms. Examples are given to illustrate advantages of our approach.