Abstract
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.
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