针对一类非线性奇异摄动系统,建立基于T-S模型的模糊奇异摄动系统模型,通过Lyapunov方法和Schur补定理,研究其稳定性、H∞性能指标和状态反馈H∞控制。将系统稳定性分析和状态反馈H∞控制器的设计,归结为求解一组与摄动参数ε无关的线性矩阵不等式问题,可以避免由ε引起数值求解的病态问题。该方法适用于标准和非标准非线性奇异摄动系统,仿真实例说明该方法的有效性。 For a class of nonlinear singularly perturbed systems, a fuzzy singular perturbation system model based on T-S model is established. Its stability, H∞ performance index and state feedback H∞ control are studied by Lyapunov method and Schur complement. The stability analysis of the system and the design of the state feedback H∞ controller can be summarized as solving a set of linear matrix inequalities that are independent of the perturbation parameter ε, which can avoid the ill-posed problem of numerical solution by ε. The proposed method is suitable for both standard and non-standard nonlinear singular perturbation systems. Simulation examples show the effectiveness of the proposed method.