时滞系统的输出反馈滑模控制的一种奇异系统方法

利用一种奇异系统方法讨论了时滞系统的输出反馈滑模控制问题. 时滞系统的非线性项满足范数有界约束.首先,将滑动模态与线性切换面作为一个奇异时滞系统,基于奇异时滞系统的稳定性理论, 给出滑动模态稳定及切换面存在的线性矩阵不等式(Linear matrix inequality, LMI)充分条件.然后,给出使得系统闭环渐近稳定的静态输出反馈滑模控制器的设计方法,此控制器保证闭环 系统有限时间到达切换面.最后,用数值算例验证本文方法的有效性和正确性.

A Singular System Approach to Output Feedback Sliding Mode Control for Time-delay Systems

In this paper, the static output feedback sliding mode control for time-delay systems is discussed based on a singular system approach. First, the sliding mode dynamics and the linear switching surface are treated as a singular time-delay system. Based on stability theory of singular time-delay systems, a linear matrix inequality (LMI) sufficient condition is proposed, which guarantees the stability of the sliding mode dynamics and the existence of the switching surface. Then, a static output feedback sliding mode controller is designed such that the closed-loop system is asymptotically stable and the state trajectories of the closed-loop system are convergent to the switching surface in a finite time. At last, two numerical examples are given to illustrate the effectiveness of the proposed method.