gap度量下线性时变系统的鲁棒性  

Robustness for Linear Time-varying Systems Using the Gap Metric

作　　者：徐晓萍[1] 石岩月[1] Xiao Ping;XU Yan;Yue SHI(School of Mathematical Sciences,Ocean University of China,Qingdao 266100,P.R.China)

机构地区：[1]中国海洋大学数学科学学院,青岛266100

出　　处：《数学学报（中文版）》2021年第6期881-894,共14页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11701537);中央高校基本科研业务费(201964007)。

摘　　要：本文主要在套代数框架下研究了线性时变系统的鲁棒稳定性.当系统和控制器具有gap度量下相互独立的扰动时,应用系统图和控制器图的三角形式,给出了该类系统鲁棒稳定的充分条件.进一步地,还给出了多个系统同时鲁棒稳定的充分条件.数值结果表明结论是有效的.We mainly study the robust stability for linear time-varying systems within the framework of nest algebra.We consider the robust stability when the system and controller are subject to independent uncertainties measured by the gap metric,and a sufficient condition is obtained by using the trigonometric structure of the graphs about the plant and the controller.Furthermore,we also obtain some sufficient conditions for the simultaneously robust stability of several linear time-varying systems.The numerical example shows that our conclusion is effective.

关 键 词：稳定性 套代数 无穷维线性时变系统 gap度量 

分 类 号：O177.1[理学—数学]