Robust stability criterion for uncertain stochastic systems with time-varying delay via sliding mode control

This paper is focused on sliding mode control (SMC) for uncertain stochastic systems with time‐varying delay. Both time‐varying parameter uncertainties and stochastic perturbations may appear in the controlled system. A new integral‐type switching surface function is first constructed. Then, a sufficient condition for the existence of sliding surface is established in terms of linear matrix inequalities (LMIs) by employing some free weighting matrices, which guarantees the robustly stochastically stable of the sliding mode dynamic system with time‐varying delay for all admissible uncertainties. Moreover, a SMC law is synthesized to drive the system state trajectories onto the predefined switching surface in a finite time. Finally, a simulation example is provided to illustrate the effectiveness of the proposed theory.