Linear Time Computation of QFT Feasible Regions

This paper represents ongoing research to reduce the computational cost of implementations of quantitative feedback theory (QFT), using ideas from Kharitonov stability theory and the theory of algorithms. By limiting our analysis to the simple case of a plant transfer function with denominator uncertainty, we gain insight into the problem of determining tracking, robust stability and actuator bounds for QFT design. A coordinate transformation allows us to exploit symmetry to reduce the computational time for the problem. This approach can be applied to more general uncertainty structures and is a main contribution of this paper. Our analysis demonstrates the importance of estimating asymptotic bounds on computational time, as is standard in algorithmic analysis. We obtain a linear time algorithm by dividing the compensator plane into twelve different regions, each of which shares critical points of a value set needed in the computation of QFT bounds. We illustrate our algorithm with a simple position control system.