Sensitivity tradeoffs for multivariable plants

This paper gives a characterization of the smallest upper bound on the norm of the sensitivity matrix over a frequency interval, with the constraint that the norm remain bounded at all frequencies. The matrix Nevanlinna-Pick interpolation theory is applied to give a necessary and sufficient condition for the existence of a sensitivity matrix meeting the upper bound conditions on the -axis, and the matrix Nevnnlinna-Pick algorithm is used to compute the bounds. A scalar example is also presented to demonstrate the tradeoffs between the bounds inside and outside a given operating frequency band.