不确定关联奇异系统分散鲁棒H∞控制

Design of robust decentralized H∞ control for uncertain interconnected descriptor systems

本文研究了不确定关联奇异系统的分散鲁棒H∞控制问题。假定不确定性是时不变、范数有界,且存在于系统和控制输入矩阵中。基于有界实引理,推导出了使不确定关联奇异系统能鲁棒镇定,且满足一定的性能指标的充分条件,即非线性矩阵不等式条件。采用两步同伦法迭代来求解该非线性矩阵不等式（NMI）。首先,通过逐步对控制器的系数矩阵加上结构限制,计算出当确定性不存在时的标称系统的分散H∞控制器。然后,逐步改变标称系统分散控制器的系数,计算出不确定性参数存在时,分散鲁棒H∞控制器。在每一阶段,每一次迭代过程中,通过交替固定NMI的一个变量,使NMI转变为线性矩阵不等式（LMI）。数值例子说明了所提出的方法的有效性。

The uncertainties were assumed to be time-invariant, norm-bounded, and in both the system and control input matrices. The interest was focused on dynamic output feedback. Based on a bounded real lemma, a sufficient condition for an uncertain interconnected descriptor system to be robustly stabilizable with a specified disturbance attenuation level, was derived in terms of a nonlinear matrix inequality （NMI）. A two-stage homotopy method was used to solve the NMI iteratively. First, a decentralized controller for the nominal descriptor system was computed by imposing block-diagonal constraints on the coefficient matrices of the controller gradually. Then, the decentralized controller was modified, again gradually, to cope with the uncertainties. On each stage, groups of variables were fixed alternately at the iterations to reduce the NMI to linear matrix inequalities （ LMIs）. An example was given to show the usefulness of this method.