基于输出反馈的不确定非线性系统模糊鲁棒H∞控制

摘要

This paper is concerned with a fuzzy robust H∞ control problem via output feed-back for a class of uncertain nonlinear systems. The uncertain nonlinear systems are represented by fuzzy Takagi-Sugeno (T-S) model, and a fuzzy controller is de-signed based on the state observer. A sufficient condition for the existence of fuzzy controller is given in terms of the linear matrix inequalities (LMIs) and the adaptive law. Based on Lyapunov stability theorem, the proposed fuzzy control scheme such that the desired H∞performance is achieved in the sense that all the closed-loop signals are uniformly ultimately bounded (UUB). Simulation results indicate the effectiveness of the developed control scheme. In this paper, a less conservative fuzzy tracking controller is proposed, where the matching condition and the upper bound are avoided. Comparing with the existing works, the dimension of the LMIs of this paper is reduced.%本文针对一类不确定非线性系统，研究了基于输出反馈的模糊鲁棒H∞控制问题。根据模糊T-S模型表征不确定非线性系统，基于状态观测器设计模糊控制器。由线性矩阵不等式和自适应律给出了模糊控制器存在的充分性条件。基于Lyapunov稳定性理论，提出的模糊控制方案在所有闭环信号最终一致有界意义下实现了期望的H∞性能。仿真结果表明了该方案的可行性。本文所提出的模糊跟踪控制器松弛了保守性，避免了匹配条件和上界。与已有的工作相比，本文约简了线性矩阵不等式的维数。