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模糊奇异摄动系统及其稳定性分析与综合
引用本文:刘华平,孙富春,何克忠,孙增圻.模糊奇异摄动系统及其稳定性分析与综合[J].自动化学报,2003,29(4):494-500.
作者姓名:刘华平  孙富春  何克忠  孙增圻
作者单位:1.清华大学计算机科学与技术系智能技术与系统国家重点实验室,北京
基金项目:NationalNaturalScienceFoundationofP .R .China (6 0 0 84 0 0 2and 6 0 174 0 18),NationalKeyProjectforBasicResearchofP .R .China(G2 0 0 2cb312 2 0 5 ),NationalExcellentDoctoralDissertationFoundationofP .R .China(2 0 0 0 4 1),NationalNatura
摘    要:通过扩展常规Takagi-Sugeno模糊系统,定义了一类模糊奇异摄动系统,利用矩阵不等 式表达出了在摄动参数足够小时的闭环稳定性.镇定并行分布式补偿控制器增益和共同的Lyapunov 函数可利用两步法得到,并可分别归结于一组线性矩阵不等式和双线性矩阵不等式,后者 可以利用迭代线性矩阵不等式方法有效地求解.文末给出了数值和仿真实例.

关 键 词:模糊系统    线性矩阵不等式    并行分布式补偿    奇异摄动
收稿时间:2002-8-20

Controller Design and Stability Analysis for Fuzzy Singularly Perturbed Systems
LIU Hua-ping,SUN Fu-chun,HE Ke-zhong,SUN Zeng-qi.Controller Design and Stability Analysis for Fuzzy Singularly Perturbed Systems[J].Acta Automatica Sinica,2003,29(4):494-500.
Authors:LIU Hua-ping  SUN Fu-chun  HE Ke-zhong  SUN Zeng-qi
Affiliation:1.State Key Laboratory of Intelligent Technology and Systems,Department of Computer Science and Technology,Tsinghua University,Beijing
Abstract:This paper defines a fuzzy singularly perturbed system by extending the ordinary Takagi Sugeno fuzzy model. Stability conditions for the fuzzy singularly perturbed systems for all small enough values of a singular perturbation parameter are derived and represented in terms of a set of matrix inequalities. By the proposed two stage procedure, the stable parallel distributed compensation (PDC) feedback gains and a common Lyapunov function can be found. The outcome of the stabilization problem is recast into linear matrix inequalities(LMIs) and bilinear matrix inequalities(BMIs) in each stage respectively. The resulting BMIs can be effectively solved by the proposed iterative linear matrix inequality approach. Furthermore, numerical examples and simulation results are given to verify the effectiveness of the algorithms proposed above.
Keywords:Fuzzy systems  linear matrix inequalities  parallel distributed compensation  singular perturbation  
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