Abstract
A multivariable feedback system y(s)=G(s)x(s), x(s)=u(s)-F(s)y(s) is treated where G(s) is the transfer function matrix of a plant and F(s)=diag(f1(s), …, fn(s)) is that of a controller. A new bound for the transfer function hk(s) that relates yk(s) to uk(s) when the k-th loop is open but the other loops are closed is given. The main result reads: |hk(s)-gkk(s)|<ak(s)if|fj(s)-1+gjj(s)|>aj(s)(j=1, …, n;j≠k). Here, A=diag(a1(s), …, an(s)) is such a matrix that A-B is a semi-M-matrix and B=(bjl) is given by bjj=0, bjl=|gj(s)|(j≠l). A method to determine A when B is given is also presented. The result is useful for the design of multivariable systems.
