Efficient Algorithm for the Generation of QFT Bounds for Plants With Affinely Dependent Uncertainties

Abstract

This paper presents an efficient algorithm for the generation of quantitative feedback theory (QFT) bounds for plants with affinely dependent uncertainties. For a plant with m affinely dependent uncertainties, it is shown that whether a point in the complex plane lies in the QFT bound for a frequency-domain specification at a given frequency can be tested by checking if m2m−1 one-variable quadratic equations corresponding to the edges of the domain box are all non-negative on the interval [0,1]. This test procedure is then utilized along with a pivoting procedure to trace out the boundary of the QFT bound with a prescribed accuracy or resolution. The developed algorithm can avoid the unfavorable trade-off between the computational burden and the accuracy of QFT bounds. Moreover, it is efficient in the sense that no root-finding and iterative procedures are required. Numerical examples are given to illustrate the proposed algorithm and its computational superiority.