时滞模糊奇异摄动系统状态反馈H_∞控制

State Feedback H_∞ Control for Fuzzy Time-delay Singularly Perturbed Systems

针对一类非线性奇异摄动系统,建立基于T-S模型的时滞模糊奇异摄动系统模型,通过Lyapunov方法和Schur补定理,研究其状态反馈H∞控制。将系统状态反馈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,避免由ε引起数值求解的病态问题。所得控制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。

As to a class of nonlinear singularly perturbed systems, the model of fuzzy time-delay singularly perturbed systems based on T-S model was built. The state feedback H∞ control of the system was investigated by Lyapunov approach and Schur complement theorem. The design of the state feedback H∞ controller was solved by a set of the c-independent linear matrix inequalities, so the ill-conditioned problem was avoided effectively. The controller obtained enables the closed-loop systems to be stable and to achieve the given H-infinity performance. The proposed approaches can be applied to both standard and nonstandard nonlinear singularly perturbed systems. A simulation example illustrates the approaches.