杜鑫,侯国永,贾善杰.基于平衡截断法的线性负虚系统模型降阶[J].电子测量与仪器学报,2016,30(11):1635-1646
基于平衡截断法的线性负虚系统模型降阶
Model order reduction of linear negative imaginary system based on balanced truncation
  
DOI:10.13382/j.jemi.2016.11.003
中文关键词:  模型降阶  负虚系统  平衡截断  Riccati 方程
英文关键词:model order reduction  negative imaginary system  balanced truncation  Riccati equation
基金项目:国家自然科学基金(61304143)资助项目
作者单位
杜鑫 上海大学机电工程与自动化学院上海200072 
侯国永 上海大学机电工程与自动化学院上海200072 
贾善杰 山东省电力公司经济技术研究院济南250021 
AuthorInstitution
Du Xin School of Mechatronics Engineering and Automation, Shanghai University, Shanghai 200072, China 
Hou Guoyong School of Mechatronics Engineering and Automation, Shanghai University, Shanghai 200072, China 
Jia Shanjie Shandong Electric Power Corporation Economic and Technology Research Institute,Ji’nan 250021,China 
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中文摘要:
      基于平衡截断理论来探讨线性负虚系统的模型降阶问题,针对无结构限制的一般线性负虚系统,借鉴关于正实系统模型降阶的现有方法,提出了一类基于求解负虚系统Lure方程组的平衡截断模型降阶算法,通过分析负虚系统Lure方程组平衡解的奇异值特性以及相应的降阶模型参数矩阵秩特性,指出了这类算法在负虚系统模型降阶中所存在的局限性;为克服这一局限,进一步提出了基于同时求解系统Lure方程和系统Lyapunov方程的平衡截断模型降阶算法,该算法可对任意线性负虚系统生成满足负虚特性的降阶模型;还给出这两类算法下的模型逼进的误差上界估计。针对带有二级结构和对称系统参数矩阵的线性负虚系统,基于合同变换法给出了一类保持系统负虚性和结构特征的平衡截断算法,并对理论结果的正确性和算法的有效性通过若干数值算例进行了说明。
英文摘要:
      The negative imaginary preserving model order reduction of linear negative imaginary systems in the balancing related framework is discussed in the paper. For general linear negative imaginary systems, two negative imaginary preserving balanced truncation (NIBT) methods are proposed. One is a Lur’e type NIBT, which is based on solutions of a couple of negative imaginary Lur’e equations. It is revealed that the Lur’e type NIBT suffers from applicability limitation due to some special structural properties of the Lur’e type balanced realization. To remove the limitation, another Lur’e/Lyapunov type NIBT is developed. Both of these NIBT methods preserve the negative imaginary property. Moreover, the approximation error estimation with regards to the NIBT methods are carried out and corresponding error bounds are provided. For second order negative imaginary systems, we show that the well known congruence trans formation based balanced truncation preserve the negative imaginary property, under some mild assumptions on the system parameter matrices. Finally, the numerical examples are included for illustration.
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