MIMO Nyquist interpretation of the large gain theorem. Issue 10 (2nd October 2020)

• Record Type: Journal Article
• Authors: Caverly, Ryan James; Pates, Richard; Bridgeman, Leila Jasmine; Forbes, James Richard
• Is Part Of: International journal of control. Volume 93:Issue 10(2020)
• Page Start: 2326
• Page End: 2335
• Publication Date: 2020-10-02
• Subjects: Large gain theorem -- Nyquist stability criterion -- linear systems -- stability of feedback interconnections -- input-output stability -- minimum gain -- robust control; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2018.1554911
• Languages: English
• ISSNs: 0020-7179

Abstract

Abstract : The Large Gain Theorem is an input-output stability result with intriguing applications in the field of control systems. This paper aims to increase understanding and appreciation of the Large Gain Theorem by presenting an interpretation of it for linear time-invariant systems using the well-known Nyquist stability criterion and illustrative examples of its use. The Large Gain Theorem is complementary in nature to the Small Gain Theorem, as it uses a lower bound on the gain of the open-loop system to guarantee closed-loop stability, rather than an upper bound on the gain of the open-loop system. It is shown that the stipulations of the Large Gain Theorem ensure that the multi-input multi-output Nyquist stability criterion is satisfied. Numerical examples of minimum gain and systems that satisfy the Large Gain Theorem are presented, along with examples that make use of the Large Gain Theorem to guarantee robust closed-loop stability.