A note on the fundamental robustness theorem of Lehtomaki

Abstract

Using a modified Nyquist contour, it is shown how to eliminate one of the conditions in Lehtomaki's fundamental robustness theorem [4]. The condition requires that the nominal open-loop characteristic polynomial be zero at each point on the imaginary axis where the perturbed open-loop characteristic polynomial has a root. Furthermore, the fundamental theorem is generalized to handle nonsquare transfer matrices as well as nonunity linear output feedback. To obtain this generalization a multivariable Nyquist stability criterion for nonsquare transfer matrices is proved.