基于LMI方法的MIMO系统鲁棒D-稳定的频域判定

1.
北京大学力学与工程科学系,北京 100871;2.上海师范大学应用数学系,上海 200234;3.北京 1303信箱15分箱,北京 100073;4.兰州 53信箱601分箱,兰州 730070

基金项目: 中国博士后科学基金资助项目

Frequency Domain Criteria for Robust D-Stability of MIMO Systems Based on LMI Method

1.
Department of Mechanics and Engineering Science, Peking University, Beijing 100871, P. R. China;

摘要: 研究了具有结构不确定性的多输入多输出(MIMO)系统的鲁棒D-稳定性判定问题．首先提出了系统的3种数学模型，包括凸多面体型多项式矩阵模型、多线性型多项式矩阵模型和反馈型多项式矩阵模型．然后分析了各模型在参数空间中的凸性，从而将系统的稳定性检验问题转化为线性矩阵不等式(LMI)的可行性问题，并由此给出了D-稳定性的判定方法．
- 多项式矩阵 /
- 鲁棒D-稳定性 /
- 线性矩阵不等式(LMI) /
- 参数不确定性
Abstract: The problem of checking robust D-stability of multi-in and multi-out (MIMO) systems is studied. Three system models were introduced, i. e. multilinear polynomial matrix, polytopic polynomial matrix and feedback system model. Furthermore, the convex property of each model with respect to the parametric uncertainties was estabilished respectively. Based on this, sufficient conditions for D-stability were expressed in terms of linear matrix inequalities (LMIs) involving only the convex vertices. Therefore, the robust D-stability was tested by solving an LMI optimal problem.
- polynomial matrix /
- robust D-stability /
- linear matrix inequality /
- parametric uncertainty

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