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针对一类非线性奇异摄动系统,建立基于T-S模糊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H∞滤波问题.将系统H∞滤波器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,从而避免由ε引起数值求解的病态问题.所获得的滤波器使闭环系统渐近稳定并能达到给定的H∞性能指标.该方法适用于标准和非标准非线性奇异摄动系统,仿真实例表明了所提出方法的有效性.
For a class of nonlinear singularly perturbed systems, a fuzzy singular perturbation system model based on TS fuzzy model is established. The Lyapunov method and the Schur complement theorem are used to study the H∞filtering problem. The system H∞filter design is reduced to a set of solutions The linear matrix inequality which has nothing to do with the perturbation parameter ε avoids the ill-posed problem of numerical solution by ε, and the obtained filter makes the closed-loop system asymptotically stable and achieves the given H∞ performance index. This method is suitable for standard and Non-standard nonlinear singular perturbation system, the simulation example shows the effectiveness of the proposed method.