This paper proposes a new procedure for discretizing nonlinear systems described by Takagi-Sugeno fuzzy models. The discretization procedure consists of obtaining a linear auxiliary system that approximates the Takagi-Sugeno model over a sampling instant. By discretizing this auxiliary system, a norm bounded uncertain linear discrete-time system is found, which is capable of representing the fuzzy model. This auxiliary system, as well as the norm bounded uncertainty, is found by solving an optimization problem with Linear Matrix Inequality (LMI) constraints. To illustrate the discretization procedure, a constant state observer is synthesized based on simple LMI conditions and then applied to a real nonlinear Chua's circuit. Additionally, a state-feedback controller based on our discretization approach is synthesized and we obtain larger maximum sampling periods than other tested strategies from the literature.

本文提出了一种离散化由 Takagi-Sugeno 模糊模型描述的非线性系统的新程序。离散化过程包括获得一个线性辅助系统，该系统在采样时刻近似于 Takagi-Sugeno 模型。通过对这个辅助系统进行离散化，找到了一个范数有界不确定线性离散时间系统，它能够表示模糊模型。该辅助系统以及范数有界不确定性是通过解决具有线性矩阵不等式 (LMI) 约束的优化问题而找到的。为了说明离散化过程，基于简单的 LMI 条件合成了一个恒定状态观测器，然后将其应用于实际的非线性蔡氏电路。此外，