Abstract: In this paper,two novel approach laws called I-variable speed reaching law and m-variable speed reaching law are brought forward and the design method of VSC is given which is obtained straightforward by the reaching law method,based on the discrete time linear constant system.It is shown that under the action of the VSC on the system the reaching mode and sliding mode have changeable speeds,the good performance of reaching mode is kept and the chatter of quasi-sliding mode is weakened very well.Therefore,the performance of the closed loop system is improved.The simulation results have revealed that the design methods are effective and feasible.

Key words: variable speed reaching law； veriable structure control(VSC)； quasi-sliding mode sector； discrete system；