一类不确定广义系统的鲁棒H_∞控制

主要考虑一类具有有界扰动不确定广义系统的二次稳定问题.通过变换的方法,将比例导数反馈镇定不确定广义系统H∞控制问题转化为增广不确定广义系统的状态反馈H∞控制问题.证明了不确定广义系统比例导数状态反馈(PDSF)H∞鲁棒控制与增广系统比例状态反馈(PSF)H∞鲁棒控制问题的等价性.应用LMI方法,给出不确定广义系统具有H∞性能指标γ的充分条件及鲁棒控制器的设计方法.最后,数值例子说明定理的有效性.

Robust H∞ Control for a Class of Uncertain Singular Systems

The problem of quadratic stability is considered for a class of uncertain singular systems with norm-bounded perturbation. By transform method, the problem of control with H∞ performance index becomes a corresponding robust H∞ stabilization problem for augmented uncertain singular system. Thus, it is proved that the normalization and robust H∞ stabilization via PDSF for uncertain singular system are equivalent to the robust H∞ stabilization via PSF. Based on LMI method, the design of robust H∞ controller is given with the validity of relevant theorems illustrated by a numerical example.