自动化学报2004，Vol.30Issue(1)：1-7,7.
基于迭代线性矩阵不等式的奇异摄动系统同时镇定
Simultaneous Stabilization for Singularly Perturbed Systems via Iterative Linear Matrix Inequalities
摘要
Abstract
This paper investigates simultaneous stabilization of several linear singularly perturbed systems using a single linear state feedback controller. Simultaneous stability conditions for the singularly perturbed systems are derived and represented in terms of a set of matrix inequalities,and the stiff problem is avoided since the design procedure is independent of the small parameter.By the proposed two-stage procedure, the stable simultaneous feedback gains and Lyapunov functions can be found. The outcome of the simultaneous stabilization problem is recast into a set of bilinear matrix inequalities (BMIs) in each stage. The resulting BMIs can be effectively solved by the proposed iterative linear matrix inequality (ILMI) approach. The convergence of the algorithms is also investigated. The algorithms can be used for both standard and nonstandard singularly perturbed systems. Furthermore, numerical examples and simulation results are given to verify the effectiveness of the algorithms.关键词
线性矩阵不等式/奇异摄动/同时镇定Key words
Singular perturbation/linear matrix inequalities/simultaneous stabilization分类
信息技术与安全科学引用本文复制引用
刘华平,孙富春,何克忠,孙增圻..基于迭代线性矩阵不等式的奇异摄动系统同时镇定[J].自动化学报,2004,30(1):1-7,7.基金项目
Supported by National Natural Science Foundation of P. R. China (60084002 and 60174018), National Key Project for Basic Research of P. R. China ( G2002cb312205), National Excellent Doctoral Dissertation Foundation of P.R. China (200041), and National Natu （60084002 and 60174018）
