合成H∞动态观测器存在性问题的研究  

Study on the existence of unified H∞ dynamic observer

作　　者：唐敏 徐跃良[1] TANG Min;XU Yue-liang(School of Mathematics,Southwest Jiaotong University,Chengdu Sichuan 610000,China)

机构地区：[1]西南交通大学数学学院,四川成都610000

出　　处：《控制理论与应用》2020年第11期2451-2463,共13页Control Theory & Applications

摘　　要：本文研究了文献[24]提出的合成H∞动态观测器存在性问题,针对合成H∞动态观测器存在时需要满足的一组特殊Sylvester矩阵方程组是否有解进行了讨论,利用矩阵理论进行相关推导和证明,得到了此Sylvester矩阵方程组有解的充分必要条件,以及有解时解的结构,缩小了合成H∞动态观测器(UHDO)设计问题中参数的搜索范围,并给出了该Sylvester矩阵方程组的求解算法,最后的仿真例子通过解的结构中任意参数的不同取值,说明了对合成动态观测器的影响.In this paper, the existence of unified H∞ dynamic observer proposed by article [24] is studied. and whether there is a solution for a special set of Sylvester matrix equations which is needed by the existence of unified H∞ dynamic observer is discussed. By using the matrix theory, this paper conducts relevant derivation and demonstration, and finally finds out the necessary and sufficient conditions for the Sylvester matrix equations to have solutions, as well as the structure of solutions. It shortens the search range of parameters in the UHDO(unified H∞ dynamic observer) design problem.And gives the algorithm for solving the Sylvester matrix equations. Finally, different values of arbitrary parameters in the solution structure in the simulation case show the influence on the unified H∞ dynamic observer.

关 键 词：合成动态观测器 稳定 Hurwitz矩阵 矩阵方程组 广义逆 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]