This paper investigates an effective controller design method for discrete-time linear system with parameter uncertainty, time-varying delay, input nonlinearity and process disturbance. A novel discrete-time quasi-sliding mode control (DQSMC) scheme is mainly proposed. Since the sliding mode bound is directly involved in the DQSMC law, the chattering bound can be accurately specified. By the proposed method, the dynamic of the sliding mode is unable to escape from the pre-given neighbourhood once it is attracted into the neighbourhood, in addition, the closed-loop system achieves the almost surely stable in mean square sense. Moreover, the proposed DQSMC provides a convenient method to simultaneously regulate the convergence rates of the sliding mode and the closed-loop system. Numerical example is provided to demonstrate the effectiveness of the proposed method.

本文研究了具有参数不确定性、时变延迟、输入非线性和过程扰动的离散时间线性系统的有效控制器设计方法。主要提出了一种新颖的离散时间准滑模控制（DQSMC）方案。由于 DQSMC 定律直接涉及滑模界，因此可以准确指定颤振界。通过所提出的方法，滑模的动力学一旦被吸引到邻域中就无法逃离给定的邻域，此外，闭环系统在均方意义上实现了几乎肯定的稳定。此外，所提出的 DQSMC 提供了一种方便的方法来同时调节滑模和闭环系统的收敛速度。