时滞模糊奇异摄动系统H_∞滤波

H_∞ Filtering for Fuzzy Singularly Perturbed Systems with Time-delay

针对一类变时滞非线性奇异摄动系统,本文提出了基于T-S模糊模型的建模方法,并设计了模糊H∞滤波器,通过求解一组与摄动参数ε无关的线性矩阵不等式,获得其增益,避免了由ε引起数值求解的病态问题,所获得滤波器使闭环系统渐进稳定且达到给定的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,仿真实例说明该方法的有效性。

A modeling approach based on Takagi-Sugeno （T-S） is proposed and a fuzzy H∞ filter is developed for a class of nonlinear singularly perturbed systems with time-varying delay in states. The gains of the H∞ filter are obtained by solving a set of the e-independent linear matrix inequalities such that the ill-conditioned problem caused by the interaction of slow and fast dynamic modes is avoided effectively. The designed filter guarantees that the closed-loop fuzzy SPSs system is asymptotically stable and the prescribed level of disturbance attenuation is satisfied for sufficiently small 6. The proposed approach can be applied to both standard and nonstandard nonlinear singularly perturbed systems. A simulation example is provided to illustrate the designed procedures.