不确定奇异分布参数系统的鲁棒D稳定  

Robust D-stability for Singular Distributed Parameter Systems Subjected to Uncertainties

作　　者：赵磊[1] 孙福权[2] 任俊超[3] 李本文[4] ZHAO Lei;SUN Fu-quan;REN Jun-chao;LI Ben-wen(College of Petroleum Engineering, Liaoning Shihua University, Fushun 113001, China;a. College of Information Seienee and Engineering;b. Institute of Systems Science, Northeastern University, Shenyang 110819, Chin;3. Institute of Thermal Engineering, School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, China)

机构地区：[1]辽宁石油化工大学石油天然气工程学院,辽宁抚顺113001 [2]东北大学信息科学与工程学院,沈阳110819 [3]东北大学系统科学研究所,沈阳110819 [4]大连理工大学热能工程研究所,辽宁大连116024

出　　处：《控制工程》2018年第6期985-992,共8页Control Engineering of China

基　　金：国家自然科学基金资助项目(61203001)

摘　　要：研究奇异分布参数系统的鲁棒D稳定和D稳定化问题。通过采用配置点谱方法和差分方法,把奇异分布参数系统转换成离散奇异系统。当所有系统矩阵都存在范数有界的不确定性包括差分矩阵E。假设E对于所有允许的不确定性都是秩不变的。这样把该系统的鲁棒分析问题分为两种情况：右奇异和左奇异。基于上面两种情况提出2个充要D稳定条件。这样基于这些条件,采用增广方法,提出充分的D稳定化条件。所有得到的条件都是基于线性矩阵不等式。最后,使用非稳态1维方腔流的数学模型来证明基于两种情况提出的方法的有效性。This paper investigates the problems of robust D-stability and D-stabilization for singular distributed parameter systems with norm-bounded uncertainties in all the system matrices including that in the difference matrix E. Under the assumption that the difference matrix E is rank-invariant for all admissible uncertainties, the robustness analysis problem under consideration falls into two cases： the right-singular case and the left-singular case. Two necessary and sufficient D-stability conditions are proposed for the first and second cases. Then, based on these conditions, by using a state augmentation technique, the sufficient D-stabilization conditions are obtained for both cases. Both the D-stability and the D-stabilization conditions are proposed in terms of linear matrix inequalities. Finally, illustrative examples are given to demonstrate the application of the proposed method for both cases.

关 键 词：鲁棒D稳定 鲁棒D稳定化 不确定奇异分布参数系统 线性矩阵不等式 

分 类 号：O231.1[理学—运筹学与控制论]