Reduced-order Observer-based H_∞ Controller Design for Descriptor Systems

本文研究基于Luenberger观测器的广义系统降阶H∞控制器的设计问题,并且该观测器是关于干扰解耦的。首先是提出了广义系统H∞状态反馈控制问题的一个充要条件,并利用线性矩阵不等式方法求解出广义系统的H∞状态反馈增益。然后对该H∞状态反馈增益进行渐进降阶观测,基于广义Sylvester矩阵方程的显式通解的参数化设计方法,实现了广义系统的降阶H∞控制。本文最主要的工作是给出了相应的广义线性系统降阶H∞控制器的设计算法。在文章的最后给出了一个例子,用来说明降阶算法的有效性。This paper presents the design of a robust reduced-order Luenberger observer-based H∞ controller for the descriptor system.This observer is with disturbance decoupling.A necessary and sufficient condition for the H∞ state-feedback control problem of descriptor systems is established.Based on the parametric design approach for generalized Sylvester matrix equations,a reduced-order H∞ controller for descriptor systems is obtained.One major contribution of the present work is that a design algorithm for constructing the reduced-order H∞ controller is presented.An illustrative example is also given.福建省自然科学基金(A0510002)资助;; 厦门大学985二期信息创新平台项目资助;; 福建省新世纪优秀人才支持计划资