基于分段多项式李雅普诺夫函数的模糊系统的稳定性分析  

Stability analysis of fuzzy systems using piecewise polynomial Lyapunov function

作　　者：吴雨棠 李丽珍 胡德时 WU Yu-tang;LI Li-zhen;HU De-shi(College of Mathematics and Physics,Shanghai University of Electric Power,Shanghai 200090,China)

机构地区：[1]上海电力大学数理学院,上海200090

出　　处：《控制理论与应用》2023年第3期558-564,共7页Control Theory & Applications

基　　金：国家自然科学基金项目(61903244)资助。

摘　　要：本文采用最大型分段多项式李雅普诺夫函数研究了多项式模糊系统的闭环稳定性问题.首先,本文设计了与分段李雅普诺夫函数对应的切换模糊控制器,提出了多项式模糊模型稳定的平方和条件,同时证明了最大型分段多项式李雅普诺夫函数在函数切换点的稳定性.然后,设计了相应的路径跟踪优化算法,对本文非凸的稳定条件进行迭代求解.最后,通过两个算例进行仿真与比较,说明并验证了本文所提出结论的可行有效性.This paper is devoted to studying the closed-loop stability of polynomial fuzzy systems by using piecewise polynomial Lyapunov function.Firstly,this paper designs the switching fuzzy controller corresponding to the piecewise Lyapunov function,puts forward the sum-of-square conditions for the stability of the polynomial fuzzy model.Meanwhile,the stability of the maximum-type piecewise polynomial Lyapunov function at the switching point is proved.Then,the appropriate path-following optimization algorithm is adopted and designed to solve the nonconvex stability conditions iteratively.Finally,the simulation of two examples and the comparison vertify that the proposed conclusions are feasible and effective.

关 键 词：分段多项式李雅普诺夫函数 平方和方法 多项式模糊模型 路径跟踪算法 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]