基于LMI的离散广义系统的容许性和鲁棒镇定性

Admissibility and Robust Stabilization of Discrete Singular Systems Based on LMI

本文主要研究了离散广义系统的容许性问题.利用离散广义系统的受限等价变换,提出了一个新的使离散广义系统容许的充分必要条件.通过引入一个中间矩阵,以配置系统矩阵的部分极点的方式来保证闭环系统的正则性,并设计了一个状态反馈控制器使得闭环系统容许.利用类似方法,对不确定离散广义系统的控制器设计问题进行了相应的讨论,得到了不确定离散广义系统鲁棒镇定的充分条件.本文提出的所有方法是严格的线性矩阵不等式(LMI).两个数值例子验证了本文方法的有效性.

The admissibility issue of discrete singular systems was mainly studied.Applying restricted equivalent transformations of the discrete singular system,a new necessary and sufficient condition was proposed to ensure discrete singular system admissible.By introducing an intermediate matrix to configure partial poles of system matrix such that the closed-loop system is regular,a state feedback controller was designed to make the closed-loop system admissible.Using similar methods,the controller design problem of uncertain discrete singular systems was discussed as well,a sufficient condition of robust stabilization for uncertain discrete singular systems was obtained.All the methods proposed in this article are strictly linear matrix inequalities(LMI).Two numerical examples verify the effectiveness of the proposed methods.