For a class of discrete time systems with matched and unmatched uncertainties, a discrete integral sliding mode
control method based on the power-function is proposed in this paper. Theoretical analysis shows that, the chattering of
discrete integral sliding mode control systems can be eliminated, and the robustness against the matched and unmatched
uncertainties can be guaranteed. Under the condition that the bounds of the uncertainties of the system are unknown, one
step delayed disturbance estimation is introduced to complete the design of the controller, and the stability of the closed loop
system is proved. Simulation results show the effectiveness of the proposed method.