针对一类变时滞离散系统,基于一种新型的非线性时变准滑模面设计方案,研究了系统的鲁棒滑模控制问题.首先,给出了该种非线性切换函数的一般形式,该类准滑模面具有时变的特征,且能够动态地改善系统的运动品质.利用自由权矩阵与线性矩阵不等式技术,给出了该类时滞离散系统非线性准滑模面的设计方法,并得到了稳定的非线性准滑模面存在的充分条件；其次,基于一种改进的离散趋近律方法,设计了相应的准滑模控制器,以保证系统的状态在有限时间内到达准滑模,从而将此类非线性系统的滑模变结构控制的分析与综合问题推广到了时滞非线性系统.最后,仿真结果表明,在本文所设计的准滑模面与准滑模变结构控制器的作用下,系统的状态是稳定的,且具有响应速度快、超调量小、调节时间较小等优点,从而说明了本文所设计方法的有效性.%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. Firefly, 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.
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