A new algorithm of reaching law discrete-time sliding mode control is designed by using power-function.
Theory analysis about non-chattering is also given. As to nominal system, this algorithm can make the value of switch function reach zero speedily without chattering. As to uncertain system accorded with matching condition, this algorithm can make the value of switch function monotonously reach a certain value which is related with external disturbance. Numerical value simulation is given by using inverted pendulum model. Simulation results show that there is no chattering hundred- percent in the output of controller, the value of switch function, and the output of the controlled system. This algorithm also makes the controlled system achieve excellent dynamic performance.