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

中文关键词  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

英文关键词  piecewise polynomial Lyapunov function  sum of square  polynomial fuzzy model  path-following algorithm

中文摘要

      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.

英文摘要

      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.