Bounds for closed-loop transfer functions of multivariable systems
Bounds for closed-loop transfer functions of multivariable systems
复制标题
多变量系统闭环传递函数的界限
DOI：
10.1109/tac.1975.1101051
复制
发表时间：
1975
影响因子：
6.8
通讯作者：
O. Nwokah
中科院分区：
文献类型：
--
作者：
M. Araki;O. Nwokah
多变量反馈系统y（s）= g（s）x（s），x（s）= u（s） - f（s）y（s）y（s），而g（s）≜（g kl（s） ）是植物的转移函数矩阵，f（s）≜diag（f 1（s），...，fn（s））是控制器的新绑定。 Y J（S）给出了f J（S）◦0 k（s）对于k = 1，n; k≠j。 B≜（B KL）由B KK = 0，B kl = | g kl（s）|（k≠l）。
A multivariable feedback system y(s)=G(s)x(s), x(s) = u(s)- F(s)y(s) is treated where G(s) ≜ (g kl (s)) is the transfer function matrix of a plant and F(s) ≜ diag(f 1 (s),...,fn(s)) is that of a controller. A new bound for the transfer function h j (s) that relates y j (s) to u j (s) when f j (s)≡ 0 is given. The main result reads |h j (s)- g jj (s)| k (s)-1+ g kk (s)| > a k (s) for k = 1,... ,n; k≠j. Here, A ≜ diag(a 1 (s),...,a n (s)) is a diagonal matrix which makes A-B a semi-M-matrix where B ≜ (b kl ) is given by b kk =0, b kl = |g kl (s)| (k≠l). A similar result is also obtained for the inverse transfer function.