Nyquist Interpretation of the Large Gain Theorem

This paper presents a proof of the Large Gain Theorem using the Nyquist Stability Criterion. The minimum gain constraint stipulated by the Large Gain Theorem guarantees the open-loop transfer function encircles the point (-1,0) exactly P times in the counterclockwise direction, where P is the number of open-loop open right-half plane poles. This guarantees asymptotic stability of the feedback system, even in the presence of an unstable open-loop transfer function. The Nyquist interpretation of the Large Gain Theorem is compared to Nyquist interpretations of the Large Gain and Passivity Theorems. Applications of the Large Gain Theorem are discussed and numerical examples illustrating the concept of minimum gain and the Large Gain Theorem are presented.