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

Abstract EN

Lyapunov stability theory, variational methods, Gronwall-Bellman-typeinequalities theorem, and linear matrices inequality (LMI) technique are synthetically employed toobtain the LMI-based global stochastic exponential stability criterion for a class of time-delaysLaplace diffusion stochastic equations with large impulsive range under Dirichlet boundary value,whose backgrounds of physics and engineering are the impulsive Markovian jumping time-delaysreaction-diffusion BAM neural networks.

As far as the authors know, it is the first time to derivethe LMI-based criterion by way of Gronwall-Bellman-type inequalities, which can be easily andefficiently computed by computer Matlab LMI toolbox.

And the obtained criterion improves theallowable upper bounds of impulse against those of some previous related literature.

Moreover, anumerical example is presented to illustrate the effectiveness of the proposed methods.