基于分段模糊Lyapunov函数的模糊系统稳定性分析和保性能设计
doi: 10.3724/SP.J.1004.2008.00721 cstr: 32138.14.SP.J.1004.2008.00721
Stability Analysis and Guaranteed Cost Design of Fuzzy Systems via Piecewise Fuzzy Lyapunov Function Approach
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摘要: 针对一类 Takagi-Sugeno (T-S) 连续模糊系统, 在分析模糊系统前提规则结构信息的基础上, 研究了其稳定性和保性能设计问题. 通过将模糊 Lyapunov 函数 (FLF) 和分段二次 Lyapunov 函数 (PQLF) 结合, 构造出分段模糊 Lyapunov 函数 (PFLF), 并提出了一种新的并行分配补偿 (PDC) 控制器. 基于 PFLF 方法, 得到了线性矩阵不等式 (LMI) 形式的模糊系统分析与设计的求解方法. 该方法继承了 FLF 与 PQLF 的优点. 仿真实例表明: 该方法所得稳定性判据更为宽松, 具有更好的保性能控制效果.
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关键词:
- T-S模糊系统 /
- 分段模糊Lyapunov函数 /
- 并行分配补偿 /
- 线性矩阵不等式
Abstract: This paper deals with the stability analysis and guaranteed cost design of a class of Takagi-Sugeno (T-S) fuzzy systems. Based on the structure information of the premise rule base, a new Lyapunov function called piecewise fuzzy Lyapunov function (PFLF) is proposed by combining the fuzzy Lyapunov function (FLF) and piecewise quadratic Lyapunov function (PQLF). A new parallel distributed compensation (PDC) controller is also presented. Based on the PFLF approach, a stability analysis and guaranteed cost control design method is derived in the form of linear inequality matrix (LMI). This method inherits the advantage of FLF and PQLF. Simulation results show that the stability analysis of this method is more relaxed in addition to the much better guaranteed cost control performance. -
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