Mean square exponential stabilization analysis of stochastic neural networks with saturated impulsive input

The exponential stabilization of stochastic neural networks in mean square sense with saturated impulsive input is investigated in this paper. Firstly, the saturated term is handled by polyhedral representation method. When the impulsive sequence is determined by average impulsive interval, impulsive density and mode-dependent impulsive density, the sufficient conditions for stability are proposed, respectively. Then, the ellipsoid and the polyhedron are used to estimate the attractive domain, respectively. By transforming the estimation of the attractive domain into a convex optimization problem, a relatively optimum domain of attraction is obtained. Finally, a three-dimensional continuous time Hopfield neural network example is provided to illustrate the effectiveness and rationality of our proposed theoretical results. •The impulsive control sequence is defined by (mode-dependent) impulsive density.•Estimating attractive domain’s size is converted into solving optimization problems.•Introduce a convex set to handle mode-dependent saturated impulsive input strategies.