A new formulation of multiple-input multiple-output quantitative feedback theory

The QFT robust performance problem in its entirety may be reduced to an H_∞ problem by casting each specification as a frequency domain constraint on the nominal sensitivity function and the complementary sensitivity function. It is shown that the existence of a solution to the standard H_∞ problem guarantees a solution to the QFT problem whereas the existence of a QFT solution does not necessarily guarantee an H_∞ solution. A solution obtained via this formulation for the QFT problem is in general more conservative when compared to what may be obtained from classical QFT loopshaping. However one does not have to restrict the QFT controller to be diagonal as is usually done in MIMO QFT. In addition a simple constructive approach is provided for the design of a prefilter matrix in MIMO systems. In general the synthesis of a prefilter matrix for the MIMO case is much more involved than that of the SISO case