LMI-Based Stability Criterion for Impulsive Delays Markovian Jumping Time-Delays Reaction-Diffusion BAM Neural Networks via Gronwall-Bellman-Type Impulsive Integral Inequality

Abstract

Lyapunov stability theory, variational methods, Gronwall-Bellman-type inequalities theorem, and linear matrices inequality (LMI) technique are synthetically employed to obtain the LMI-based global stochastic exponential stability criterion for a class of time-delays Laplace diffusion stochastic equations with large impulsive range under Dirichlet boundary value, whose backgrounds of physics and engineering are the impulsive Markovian jumping time-delays reaction-diffusion BAM neural networks. As far as the authors know, it is the first time to derive the LMI-based criterion by way of Gronwall-Bellman-type inequalities, which can be easily and efficiently computed by computer Matlab LMI toolbox. And the obtained criterion improves the allowable upper bounds of impulse against those of some previous related literature. Moreover, a numerical example is presented to illustrate the effectiveness of the proposed methods.