In this paper, a new disturbance estimator-based switching function (SF) is presented dedicated to discrete-time sliding mode control (DSMC) systems with disturbances and control saturation (CS). This SF is featured by an (n+1)th-order disturbance estimator, which utilizes n+1 past disturbance terms to attain accurate disturbance rejection. Moreover, an auxiliary state is integrated into the SF to address the CS problem. One uniqueness of the developed method is that it is capable of achieving the ideal quasi-sliding mode and produces a zero-convergence error of the SF under the influence of disturbances and CS, which is rarely realized in DSMC methods. In addition, system states dynamics is rigorously analysed adopting the Lyapunov technique. The feasibility and virtue of the designed results are verified by a numerical example.

在本文中，提出了一种新的基于扰动估计器的开关函数（SF），该函数专用于具有扰动和控制饱和（CS）的离散时间滑模控制（DSMC）系统。该SF的特征在于（n +1）阶干扰估计器，它利用n+1过去的干扰项以获得准确的干扰抑制。此外，辅助状态被集成到SF中以解决CS问题。所开发方法的独特之处在于它能够实现理想的准滑动模式，并在干扰和CS的影响下产生SF的零收敛误差，这在DSMC方法中很少实现。此外，采用Lyapunov技术对系统状态动力学进行了严格分析。通过数值算例验证了设计结果的可行性和优越性。