A new discrete reaching condition of quasi-sliding mode (QSM) and generalized discrete reaching law with different convergence rates are proposed in this paper. The superiority is that they can ensure the faster convergence rate and shorten the reaching phase of the sliding variable by adjusting a positive integer value. The relationship between the generalized discrete reaching law parameters and the width of QSM domain are investigated for both positive and negative decay factors, respectively. Under proper choices of the parameters, the generalized discrete reaching law will satisfy the proposed new reaching condition and guarantee the QSM motion. Finally, a simulation example is given to illustrate the usefulness and superiority of the results.

提出了一种新的准滑模(QSM)离散到达条件和具有不同收敛速度的广义离散到达律。优点是它们可以通过调整一个正整数值来保证更快的收敛速度并缩短滑动变量的到达阶段。分别针对正衰减因子和负衰减因子研究了广义离散到达律参数与 QSM 域宽度之间的关系。Under proper choices of the parameters, the generalized discrete reaching law will satisfy the proposed new reaching condition and guarantee the QSM motion. 最后给出一个仿真实例来说明结果的有用性和优越性。