Nonlinear quasi-sliding-mode robust control for discrete-time systems with time-delay
时滞离散时间系统的非线性准滑模鲁棒控制

The robust sliding mode control is investigated for a class of discrete-time systems with time-varying delay, which is based on a novel nonlinear time-varying quasi-sliding surface design scheme. Firstly, the general form of the nonlinear switching function with time-varying feature is given, which can dynamically improve the quality of its motion. By using the free weighting matrix and linear matrix inequality technique, we propose a design method for the nonlinear quasi-sliding surface, and obtain a sufficient condition of asymptotical stability for the nonlinear sliding motion. Secondly, the quasi-sliding mode controller is designed based on the improved discrete reaching law to ensure the state of the system for reaching the quasi-sliding mode in a finite time. Thus, the quasi-sliding-mode variable-structure control (VSC) for such nonlinear system is extended to the nonlinear control with time-delay. Simulation validates that the dynamic behavior of the system is stable with rapid response, low overshoot, less settling time, when employing the proposed quasi-sliding surface and quasi-sliding mode VSC.