模糊奇异摄动系统H_∞分析与综合

H_∞ Analysis and Synthesis of Fuzzy Singularly Perturbed Systems

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。

As to a class of nonlinear singularly perturbed systems, the model of fuzzy singularly perturbed systems based on T-S model was built. The stability, H∞ performance and state feedback H∞ control of the system were researched by Lyapunov approach and Schur complement theorem. The analysis of stability and the design of the state feedback H∞ controller were solved by a set of the ε-independent linear matrix inequalities, so the ill-conditioned problem was avoided effectively. The proposed approaches can be applied to both standard and nonstandard nonlinear singularly perturbed systems. A simulation example is provided to illustrate the approaches.