切换多项式模糊系统的静态输出反馈控制器设计  

Static Output Feedback Controller Design for Switching Polynomial Fuzzy-Model-Based Systems

作　　者：王祥 李丽珍 杨帆 WANG Xiang;LI Lizhen;YANG Fan(College of Mathematics and Physics,Shanghai University of Electric Power,Shanghai 200090)

机构地区：[1]上海电力大学数理学院,上海200090

出　　处：《系统科学与数学》2025年第1期56-71,共16页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金项目(61903244)资助课题。

摘　　要：文章研究了切换多项式模糊系统的静态输出反馈控制器的设计问题.文章基于切换的操作子域以及切换李雅普诺夫函数设计了多项式静态输出反馈控制器,使系统达到渐近稳定.同时考虑了隶属函数的边界信息并且引入了多项式松弛矩阵,降低了稳定性条件的保守性.随后运用优化算法将非凸的控制算法转化为凸条件,该条件可以通过SOSTOOLS求解.最后利用数值仿真验证了文章控制器设计方法的有效性.This paper studies static output feedback controller designed for the switching polynomial fuzzy model-based control system.This paper uses the switch-ing method which based on the operation sub-domains and the switching Lyapunov function to design the polynomial static output feedback controller,so that the system can achieve asymptotic stability.At the same time,the boundary information of the membership function is considered and the slack polynomial matrices are introduced,which reduces the conservatism of the stability conditions.Then,the optimization algorithm is used to transform the non-convex control algorithm into the convex con-ditions,which can be solved by SOSTOOLS.Finally,a numerical simulation is used to verify the effectiveness of the controller design method in this paper.

关 键 词：多项式模糊系统 切换静态输出反馈控制器 切换多项式李雅普诺夫函数 松弛矩阵 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]