Linear time computation of feasible regions for robust compensators
M. Sami Fadali, L.E. LaForge · International Journal of Robust and Nonlinear Control · 2001
Abstract We introduce an application of computational geometry, including figures of merit standard in the analysis of algorithms, to the design of robust control systems. With respect to system transfer function magnitude, we show how to compute feasible regions for compensators whose plant transfer function is the ratio of uncertain interval polynomials. Our solution sweeps the Minkowski quotient set of the corresponding Kharitonov rectangles. Enumerating the winding numbers of Minkowski sum convolution curves, we obtain optimal, linear time algorithms that eliminate three factors from the execution inefficiency of traditional gridding approaches. We illustrate with examples pertinent to quantitative feedback theory (QFT). Copyright © 2001 John Wiley & Sons, Ltd.