Abstract
Regions on the complex plane are employed in a version of the Nyquist stability test for control systems when the system model contains parameter uncertainties. Generally, the uncertain parameters are real and bounded and appear as numerator and denominator coefficients in a rational function of frequency. Through the function, the parameters describe a set of model points at each frequency. The problem of locating such sets is defined for a model useful in describing the frequency response of physical processes. A new algorithm for locating region boundaries enclosing the set of models is presented. Boundary points connected by line segments are determined by the algorithm. The algorithm offers two principal advantages over previously available methods: (1) The region boundaries are guaranteed to enclose the set of models, and (2) the algorithm preserves concave sides on the region enclosing the set.
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