This study investigates the problem of state feedback impulse robust stabilization and applies \(H_{\infty }\) control techniques to linear discrete-time systems with impulse characteristics. Furthermore, it explores their extensions in the context of neural networks. The proposed framework is novel in its integration of impulsive dynamics, stochastic disturbances, and state feedback control within a unified discrete-time setting, significantly generalizing existing results that are limited to either continuous time or impulse free. The Lyapunov function is introduced, and sufficient conditions are derived to ensure robust exponential stability of the closed-loop system under state feedback control. A robust \(H_{\infty }\) performance index is also defined to evaluate system performance. The findings are generalized from discrete-time stochastic impulsive systems to systems incorporating both state control and external disturbances. Finally, the effectiveness of the proposed methods is validated through a gene regulatory network model and a numerical example.
