基于非二次Lyapunov函数的不确定模糊系统鲁棒H_∞控制

Robust H_∞ control for uncertain fuzzy systems based on non-quadratic Lyapunov function

研究一类具有参数不确定的T-S模糊系统鲁棒镇定和鲁棒H_∞控制问题.基于一种非二次Lyapunov函数和非并行分布补偿(non-PDC)控制律,给出以线性矩阵不等式(LMI)形式表示的闭环系统鲁棒镇定的充分条件及相应的鲁棒H_∞控制器设计方法.与采用多个二次Lyapunov函数的模糊混合方法不同,在所提出的方法中,隶属函数对时间导数无需附加额外的要求.此外,对具有输入约束的H_∞控制器设计问题进行探讨,并通过一个数值仿真实验验证所提出方法的有效性.

The problems of robust stabilization and robust H∞ control are discussed for a class of T-S fuzzy systems with parametric uncertainties. Based on a non-quadratic Lyapunov function and nonparallel distributed compensation（nonPDC） control laws, the sufficient condition of robust stabilization of a closed-loop system is derived in terms of linear matrix inequalities（LMIs）, and a design procedure for the responding robust H∞ controller is also provided. Unlike previous approaches using a fuzzy blending of multiple quadratic Lyapunov functions, the time-derivatives of the membership functions can be derived without imposing additional requirements in the proposed approach. Moreover, the problem of H∞ controller design with input constraint is also discussed. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.