On the Generation of QFT Bounds for General Interval Plants

Considered in this paper is the question of synthesizing a fixed compensator for an interval plant so that (i) robust stability and (ii) robust disturbance rejection in the sense of Quantitative Feedback Theory (QFT) are attained. As expected, the problem reduces to one of loop shaping a nominal transfer function that avoids a set of frequency dependent forbidden regions while simultaneously stabilizing the nominal plant. It is shown that for the class of interval plants considered, the QFT boundaries (i.e., the magnitude restrictions on the nominal loop transfer function at each phase for a given frequency) can be explicitly computed by solving a number of simultaneous inequalities at each frequency. These results yield computationally efficient algorithms mainly because the need for the usual one dimensional search on the magnitude of the nominal loop transfer function has been completely removed.