线性系统传递函数阵H_∞范数的性质及计算  

Properties and Computation of Linear System Transfer Matrix H_∞-norm

作　　者：徐跃良[1] 李治[2] 

机构地区：[1]西南交通大学理学院,四川成都610031 [2]西南交通大学电气工程学院,四川成都610031

出　　处：《西南交通大学学报》2004年第5期684-686,695,共4页Journal of Southwest Jiaotong University

摘　　要：建立了判断系统[A,B,C,D]与系统[A+BR-1DTC,BR-1/2,(I+DR-1DT)1/2C,0]传递函数阵H∞范数是否小于1的等价定理.用此定理得到了判断系统[A,B,C,D]是否稳定的另一定理.用此定理使有关判断系统[A,B,C,D]是否稳定及其传递函数阵的H∞范数大小的有关定理的证明得到简化.给出了计算系统[A,B,C,D]传递函数阵H∞范数的算法.An equivalence theorem was derived to determine if the transfer matrix H_∞-norm between two linear systems [A,B,C,D] and [A+BR^(-1)D^TC,BR^(-1/2),(I+DR^(-1)D^T)^(1/2)C,0] is smaller than 1. This theorem was then used to derive another theorem about the stability of system [A,B,C,D]. This equivalence theorem simplifies the proof of the theorem about the stability of system [A,B,C,D] and determination of H_∞-norm. An algorithm for computing the H_∞-norm of the transfer matrix of system[A,B,C,D] was presented.

关 键 词：传递函数 H∞范数 线性系统 稳定性 Riccafi不等式 RICCATI方程 

分 类 号：O231[理学—运筹学与控制论]