This paper is concerned with the design of H∞ observers for fuzzy system with immeasurable state variables via a new Lyapunov function. By decomposing the space of premise variables into crisp regions and fuzzy regions, piecewise fuzzy H∞ observers are established at different instants to cope with the challenges caused by the mismatch of the premise variables and exogenous disturbances. Based on the proposed new Lyapunov functions that depend on the different regions where the premise variables are located, sufficient conditions in terms of linear matrix inequalities are obtained to guarantee the stability and desired performance of the error systems. Finally, a simulation example is provided to show that the new design technology proposed in this paper achieves better H∞ performance than the existing design methods.

中文翻译：

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$H_{\infty }$ 通过新 Lyapunov 函数进行具有不可测状态变量的模糊系统的观测器设计


本文关注的是通过新的 Lyapunov 函数设计具有不可测状态变量的模糊系统的 H∞ 观测器。通过将前提变量的空间分解为清晰区域和模糊区域，在不同时刻建立分段模糊H∞观测器，以应对前提变量不匹配和外生干扰带来的挑战。基于所提出的取决于前提变量所在不同区域的新李雅普诺夫函数，获得了线性矩阵不等式方面的充分条件，以保证误差系统的稳定性和期望性能。最后，提供了一个仿真例子，表明本文提出的新设计技术比现有的设计方法取得了更好的H∞性能。