分散H_2/H_∞控制的LMI方法

LMI METHODS FOR DECENTRALIZED H 2/H ∞ CONTROL

描述了大系统分散Ｈ２／Ｈ∞状态反馈控制问题，提出了存在分散Ｈ２／Ｈ∞状态反馈控制器的参数化定理和２种设计方法：直接线性矩阵不等式（ＬＭＩ）方法和迭代ＬＭＩ（ＩＬＭＩ）方法，并用实例说明了这２种方法的应用．理论和实验结果表明，所获得的状态反馈矩阵具有块对角结构，闭环系统稳定且能优化闭环传递函数的Ｈ２／Ｈ∞性能指标．

This paper provides two methods to design decentralized state feedback suboptimal controllers based on H 2/H ∞ theory for large-scale systems. In the paper, the problem of decentralized H 2/H ∞ state feedback control is described, and the parametrization theorem for state feedback controller where decentralized H 2/H ∞ exists is offered and two methods based on linear matrix inequality(LMI) are proposed to solve the problem : the direct LMI approach and iterative LMI(ILMI) approach. The controller obtained has the block diagonal structure, ensures the closed-loop system asymptotically stable and offers an H 2/H ∞ perform index optimized. The given example shows the applications of the methods.