| 基于迭代线性矩阵不等式的奇异摄动系统同时镇定 |
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| 引用本文： | 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. |
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| 作者姓名： | 刘华平 孙富春 何克忠 孙增圻 |
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| 作者单位： | 1.清华大学计算机科学与技术系,北京; |
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| 基金项目： | 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 Natural Sci |
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| 摘 要： | 研究了采用一个线性状态反馈控制器镇定多个线性奇异摄动系统的问题.同时镇定条
件可以表达为一组矩阵不等式条件,所得条件与摄动参数无关,从而有效地回避了病态问题.采
用基于快慢分解的两步法可以得到镇定控制器增益和相应的Lyapunov函数.而在每一步需要利
用迭代线性矩阵不等式技术求解相应的双线性矩阵不等式,相关定理研究了算法的收敛性.本文
所得结论可同时适用于标准与非标准奇异摄动系统.文末给出了相应的仿真算例.
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| 关 键 词： | 线性矩阵不等式 奇异摄动 同时镇定 |
| 收稿时间： | 2003-1-7 |
Simultaneous Stabilization for Singularly Perturbed Systems Via Iterative Linear Matrix Inequalities |
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| LIU Hua-Ping,SUN Fu-Chun,HE Ke-Zhong,SUN Zeng-Qi.Simultaneous Stabilization for Singularly Perturbed Systems Via Iterative Linear Matrix Inequalities[J].Acta Automatica Sinica,2004,30(1):1-7. |
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| Authors: | LIU Hua-Ping SUN Fu-Chun HE Ke-Zhong SUN Zeng-Qi |
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| Affiliation: | 1.Department of Computer Science and Technology,Tsinghua University,Beijing;State Key Laboratory of Intelligent Technology and Systems,Beijing |
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| 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. |
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| Keywords: | Singular perturbation linear matrix inequalities simultaneous stabilization |
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