Chattering-free adaptive sliding mode control for uncertain delayed stochastic systems with impulsive dynamics

This paper develops a chattering-free sliding mode control framework for uncertain stochastic systems subject to hybrid dynamics, including time-varying delays and impulsive perturbations. A novel integral sliding surface is designed to incorporate time-varying delays, parametric uncertainties, and impulsive perturbations, thereby unifying the analysis of continuous and discrete dynamics. Furthermore, the proposed adaptive scheme with the hyperbolic tangent function ensures chattering suppression while maintaining finite-time convergence from the initial moment. Additionally, sufficient conditions for the stability of the stochastic system are derived on the specified sliding surface for all admissible uncertainties, based on the Lyapunov function and the average impulsive interval. Finally, a numerical example is presented to illustrate the proposed method.