分散H_∞ 状态反馈鲁棒控制设计——LMI方法

来源期刊：中南大学学报(自然科学版)1999年第1期

论文作者：桂卫华 谢永芳 陈宁 吴敏

文章页码：88 - 91

关键词：分散鲁棒控制;状态反馈;线性矩阵不等式;迭代算法

Key words：decentralized robust control; state feedback; LMI; iterative algorithm

摘    要：应用线性矩阵不等式(LMI)方法研究了大系统分散H_∞控制问题.首先分析了分散H_∞状态反馈控制问题,然后提出了存在分散H_∞状态反馈控制器的参数化定理和一种基于LMI的迭代求解方法. 把反馈增益的设计条件转化为一个双仿射矩阵不等式,用LMI迭代算法求解分散控制器,并用实例说明了该方法的应用.结果表明,所获得的控制器具有块对角结 构,闭环系统稳定,且使其H_∞范数小于1.

Abstract: This paper is to study the decentralized H_∞ control problem for large-scale systems by linear matrix inequality (LMI) approach. In the paper, the problem of decentralized H_∞ state feedback control is described, the parametrization theorem on the existence of a decentralized H_∞ state feedback controller is addressed and an iterative method based on LMI is proposed. The design condition for the decentralized is given in the form of a biaffine matrix inequality and an iterative algorithm based on LMI is offered to obtain the decentralized controller. The controller has the block diagonal structure, and makes the closed-loop system asymptotically stable and the H_∞-norm less than 1. The given example shows the application of the method.