Robust gamma-stability analysis in a plant parameter space

Abstract

Given a characteristic polynomial whose coefficients depend polynomially on l uncertain parameters, the following robustness problem arises: Determine whether all the roots of the polynomial are located in a prescribed region Г in the complex plane for all admissible parameter values. To this end, the boundary ∂Г of Г is mapped into the parameter space. A necessary and sufficient condition for Г-stability of an operating domain in parameter space is that it contains at least one Г-stable point and is not intersected by the image of ∂Г. This condition may be tested graphically by gridding l − 2 parameters and projecting all boundaries into a two-dimensional subspace of the parameter space. Finally the method is applied to a track-guided bus with uncertain mass and velocity.