基于LMI的连续时间线性时滞系统有限频模型降阶

doi:10.3969/j.issn.1007-2861.2015.04.014

上海大学学报(自然科学版) ›› 2016, Vol. 22 ›› Issue (4): 408-420.doi: 10.3969/j.issn.1007-2861.2015.04.014

基于LMI的连续时间线性时滞系统有限频模型降阶

杜鑫1, 范培兵1, 刘夫伟2

1. 上海大学机电工程与自动化学院, 上海200072;
2. 华为技术有限公司, 上海200040

收稿日期:2014-12-02 出版日期:2016-08-30 发布日期:2016-08-30
通讯作者: 杜鑫(1983—), 男, 博士, 研究方向为模型降阶、控制系统优化设计等. E-mail: duxin@shu.edu.cn
作者简介:杜鑫(1983—), 男, 博士, 研究方向为模型降阶、控制系统优化设计等. E-mail: duxin@shu.edu.cn
基金资助:
国家自然科学基金资助项目(61304143, 61174085)

LMI based approach for finite-frequency model order reduction of continuous-time linear time-delayed systems

DU Xin1, FAN Peibing1, LIU Fuwei2

1. School of Mechatronics Engineering and Automation, Shanghai University, Shanghai 200072, China;
2. Huawei Technology Co., Ltd., Shanghai 200040, China

Received:2014-12-02 Online:2016-08-30 Published:2016-08-30

摘要/Abstract

摘要：

针对连续时间线性时滞系统, 研究了在系统工作频率范围为已知有限区间情形下的有限频模型降阶问题. 通过引入有限频域内误差传递函数的最大奇异值函数作为指标函数, 对模型逼近性能进行了刻画, 进而结合一些基础性的矩阵不等式技术和线性时滞系统性能进行分析, 得到了保持降阶模型稳定性的有限频模型逼近性能优化设计条件, 这些条件以线性矩阵不等式(linear matrix inequalities, LMIs)的形式表示, 易于检验和数值求解. 最后, 算例验证了结果的有效性.

关键词: 线性矩阵不等式, 线性时滞系统 , 有限频域 , 模型降阶

Abstract:

Model order reduction of continuous-time linear time-delayed systems over limited frequency intervals is discussed in this paper. The approximation performance is characterized by introducing an index associated with the finite-frequency maximum singular value of the error transfer function. With the aid of some fundamental matrix inequality techniques, sufficient criterion for stability of the reduced-order model and optimizing finite-frequency approximation error is derived. The model order reduction problems can be tackled by solving the corresponding linear matrix inequalities (LMIs) based optimization problems. A numerical example is given to show effectiveness of the proposed technique.

Key words: finite-frequency , linear matrix inequality (LMI), linear time-delayed system , model order reduction

杜鑫1, 范培兵1, 刘夫伟2. 基于LMI的连续时间线性时滞系统有限频模型降阶[J]. 上海大学学报(自然科学版), 2016, 22(4): 408-420.

DU Xin1, FAN Peibing1, LIU Fuwei2. LMI based approach for finite-frequency model order reduction of continuous-time linear time-delayed systems[J]. Journal of Shanghai University（Natural Science Edition）, 2016, 22(4): 408-420.

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基于LMI的连续时间线性时滞系统有限频模型降阶

LMI based approach for finite-frequency model order reduction of continuous-time linear time-delayed systems

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