As the trending law of discrete-time sliding mode control is in different forms and difficult to avoid chattering, a
general form of it is proposed, and the reaching condition without chattering is given with the academic proof, which provides
a theory basis in general for the design and research of the chattering-free trending law for the discrete-time sliding mode
control. As to the uncertain system that satisfies matching condition, the method to infer the convergent region of the switch
function and the minimal value of it without chattering are provided. The classical exponential trending law is improved as
a case of using the reaching condition without chattering based on its general form, which shows the effectiveness of the
proposed method.

trending law;chattering-free;discrete-time sliding mode control