# Nyquist Interpretation of the Large Gain Theorem

Ryan James Caverly, James Richard Forbes

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

## Abstract

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.

Original language English (US) 3606-3611 6 IFAC-PapersOnLine 50 1 https://doi.org/10.1016/j.ifacol.2017.08.702 Published - Jul 2017 Yes

### Bibliographical note

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## Keywords

• Large Gain Theorem
• Nyquist Stability Criterion
• input-output stability
• linear systems
• stability of feedback interconnections

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