Sliding mode control approach based on nonlinear integrator
采用幂次趋近律的滑模控制稳态误差界

For the sliding mode tracking control of a class of uncertain nonlinear systems using power rate reaching law, the steady-state error bounds are respectively derived when using the Slotine-form conventional sliding surface and the integral sliding surface. Mathematical relations among the sliding error bounds, system uncertainties, and parameters of the power rate reaching law are investigated by means of the Lyapunov method. Based on the BIBO stability, the relationship between the steady-state error bounds and the sliding error bounds is obtained. Finally, the mathematical expressions of the steady state tracking error bounds are derived. Moreover, for the specified steady-state error bounds, an appropriate power rate reaching law to suppress the chattering is designed. Simulation results are given and the validity of the conclusions is confirmed.