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Abstract This paper presents improved criteria for global exponential stability of reaction–diffusion neural networks with time-varying delays. A novel diffusion-dependent Lyapunov functional, which is directly linked to the diffusion terms, is suggested to analyze the role of diffusivity of each neuron on the model dynamics. In the case of Dirichlet boundary conditions, the extended Wirtinger’s inequality is employed to exploit the stabilizing effect of reaction–diffusion terms. In the framework of descriptor system approach, the augmented Lyapunov functional technique is utilized to reduce the conservatism in the values of the time delay bounds. As a result, the derived global stability criteria are more effective than the existing ones. Three numerical examples are provided to illustrate the effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]

In this paper, the problem of impulsive synchronization of two coupled delayed reaction–diffusion neural networks under aperiodic discrete measurements is revisited. Different from the previous static impulsive gain based impulsive synchronization strategy, a novel impulsive synchronization strategy using sampling-interval-dependent impulsive gains is proposed. The time-varying impulsive synchronization gains are able to adapt to the variation of sampling intervals, and thus can improve the synchronization performance. The stability analysis of the resultant synchronization error system is performed by applying an impulse-time-dependent discretized Lyapunov functions based method. Sufficient conditions for the existence of desired impulsive synchronization controllers are derived in terms of a set of linear matrix inequalities (LMIs). These conditions allow to synthesize time-varying impulsive gains. A numerical example is presented to demonstrate the effectiveness of the developed methodology. [ABSTRACT FROM AUTHOR]

In this paper, the intermittent H ∞ synchronization problem for a class of reaction-diffusion neural networks with Dirichlet boundary conditions is investigated. Different from the previous works concerning intermittent synchronization, it is assumed that the response system is subject to external disturbance, and both the control period and the control width may be variable. A switching-time-dependent Lyapunov function combined with the use of the extended Wiritinger's inequality for exploring the stabilizing role of the reaction-diffusion term is employed to analyze the exponential stability and L 2 -gain performance of the synchronization error dynamics. In the framework of linear matrix inequalities, the aperiodically intermittent H ∞ synchronization controller is designed, which guarantees internally exponential stability as well as a prescribed L 2 -gain from the exogenous input to the regulated error output. Two numerical examples are given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]