Directional sensitivity tradeoffs in multivariable feedback-systems

In this paper tradeoffs in multivariable sensitivity reduction are developed for a new Directional Sensitivity Function (DSF). The directions considered belong to direction modules of the nonminimum phase zeros (NMP) and unstable poles of the transfer matrices. The well known Bode Integral is extended for the DSF whenever the direction vector coincides with the direction module of an unstable pole. Similarly the tradeoff known as the waterbed effect is extended whenever the direction vector coincides with the direction module of a NMP zero. These results intuitively exhibit the effect of spatial positions of poles and zeros of multivariable systems on sensitivity