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MIMO Nyquist interpretation of the large gain theorem

Caverly, Ryan James ; Pates, Richard LU ; Bridgeman, Leila Jasmine and Forbes, James Richard (2020) In International Journal of Control 93(10). p.2326-2335
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.... (More)

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.

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author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
input-output stability, Large gain theorem, linear systems, minimum gain, Nyquist stability criterion, robust control, stability of feedback interconnections
in
International Journal of Control
volume
93
issue
10
pages
10 pages
publisher
Taylor & Francis
external identifiers
  • scopus:85058364672
ISSN
0020-7179
DOI
10.1080/00207179.2018.1554911
project
Scalable Control of Interconnected Systems
language
English
LU publication?
yes
id
c2fed35f-e471-4e9b-a3e6-59d94faac046
date added to LUP
2019-01-10 08:51:04
date last changed
2022-05-20 10:06:57
@article{c2fed35f-e471-4e9b-a3e6-59d94faac046,
  abstract     = {{<p>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.</p>}},
  author       = {{Caverly, Ryan James and Pates, Richard and Bridgeman, Leila Jasmine and Forbes, James Richard}},
  issn         = {{0020-7179}},
  keywords     = {{input-output stability; Large gain theorem; linear systems; minimum gain; Nyquist stability criterion; robust control; stability of feedback interconnections}},
  language     = {{eng}},
  number       = {{10}},
  pages        = {{2326--2335}},
  publisher    = {{Taylor & Francis}},
  series       = {{International Journal of Control}},
  title        = {{MIMO Nyquist interpretation of the large gain theorem}},
  url          = {{http://dx.doi.org/10.1080/00207179.2018.1554911}},
  doi          = {{10.1080/00207179.2018.1554911}},
  volume       = {{93}},
  year         = {{2020}},
}