无抖振离散滑模趋近律

针对离散滑模趋近律形式多样且容易产生高频抖振的问题，提出了离散滑模趋近律的一般形式，并给出了无抖振的到达条件及其理论证明，从一般意义上为离散滑模趋近律的设计提供了理论依据。针对满足匹配条件的不确定系统，给出了切换函数收敛域的推导方法，推导了无抖振的最小收敛域。以典型的高氏指数趋近律为例，利用无抖振的到达条件，对其一般形式进行了无抖振改进，验证了所提出方法的有效性。

Chattering-free trending law for discrete-time sliding mode control

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.