分数阶连续线性系统基于观测器的H∞状态反馈控制器的设计  

Design of Observer-Based H∞ State Feedback Controller for Fractional-order Continuous Linear Systems

作　　者：王振芳[1] 罗芳[1] 马瑞青 WANG Zhen-fang1, LUO Fang1, MA Rui-qing2(1. School of Mathematics and Computer Science, Shanxi Datong University, Datong Shanxi, 037009;2. School of Mathematics and Computer Science, Shanxi Normal University, Linfen Shanxi, 04100)

机构地区：[1]山西大同大学数学与计算机科学学院,山西大同037009 [2]山西师范大学数学与计算机科学学院,山西临汾041004

出　　处：《山西大同大学学报（自然科学版）》2018年第4期27-30,共4页Journal of Shanxi Datong University(Natural Science Edition)

基　　金：山西大同大学校级科研项目[2016K2];山西大同市科研项目[2018157]

摘　　要：讨论了分数阶连续线性系统的基于观测器的H∞控制器设计问题。首先给出了使闭环系统渐进稳定且满足H∞性能指标的充分条件。其次,采用矩阵的奇异值分解方法,以线性矩阵不等式的形式给出了基于观测器的H∞状态反馈控制器存在的充分条件。最后通过数值算例验证了方法的有效性。Absrtact：In this paper, the design of observer-based H∞ controller for fractional-order continuous linear systems is discussed.Firstly, the sufficient conditions for asymptotically stabilizing the closed-loop system and satisfying the H∞ performance index are given. Secondly, the sufficient conditions for the existence of observer-based H∞ state feedback controller are given in the form of linear matrix inequalities by using the singular value decomposition method of matrices. Finally, the effectiveness of the method is verified by numerical examples.

关 键 词：分数阶系统 基于观测器的状态反馈控制器 奇异值分解 

分 类 号：O175[理学—数学]