Extending small gain and passivity theory for large-scale system interconnections

Wynita M. Griggs; S. Shravan K. Sajja; Brian D.O. Anderson; Robert N. Shorten

doi:10.1109/acc.2012.6315476

Extending small gain and passivity theory for large-scale system interconnections

Wynita M. Griggs^*, S. Shravan K. Sajja, Brian D.O. Anderson, Robert N. Shorten

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Citations (Scopus)

Abstract

In this paper, we use classical Nyquist arguments to derive stability results for large-scale interconnections of mixed linear, time-invariant (LTI) systems. We compare our results with P. J. Moylan and D. J. Hill, Stability criteria for large-scale systems, IEEE Transactions on Automatic Control, vol. 23, no. 2, 1978, pp. 143-149. Our results suggest that, if one relaxes the assumptions on the subsystems in an interconnection from assumptions of passivity or small gain to assumptions of mixedness, then the Moylan- and Hill-like conditions on the interconnection matrix become more stringent. We also explore the stability of large-scale, time-varying interconnections of strictly positive real systems. We determine a condition that guarantees the existence of a Lyapunov function for the interconnected system.

Original language	English
Title of host publication	2012 American Control Conference (ACC)
Place of Publication	Montreal, QC, Canada
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	6376-6381
ISBN (Print)	9781457710957
DOIs	https://doi.org/10.1109/acc.2012.6315476
Publication status	Published - 2012
Event	2012 American Control Conference, ACC 2012 - Montreal, QC, Canada Duration: 27 Jun 2012 → 29 Jun 2012

Publication series

Name	Proceedings of the American Control Conference (ACC)
Publisher	IEEE
ISSN (Print)	0743-1619
ISSN (Electronic)	2378-5861

Conference

Conference	2012 American Control Conference, ACC 2012
Country/Territory	Canada
City	Montreal, QC
Period	27/06/12 → 29/06/12

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10.1109/acc.2012.6315476

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Griggs, W. M., Sajja, S. S. K., Anderson, B. D. O., & Shorten, R. N. (2012). Extending small gain and passivity theory for large-scale system interconnections. In 2012 American Control Conference (ACC) (pp. 6376-6381). (Proceedings of the American Control Conference (ACC)). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/acc.2012.6315476

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title = "Extending small gain and passivity theory for large-scale system interconnections",

abstract = "In this paper, we use classical Nyquist arguments to derive stability results for large-scale interconnections of mixed linear, time-invariant (LTI) systems. We compare our results with P. J. Moylan and D. J. Hill, Stability criteria for large-scale systems, IEEE Transactions on Automatic Control, vol. 23, no. 2, 1978, pp. 143-149. Our results suggest that, if one relaxes the assumptions on the subsystems in an interconnection from assumptions of passivity or small gain to assumptions of mixedness, then the Moylan- and Hill-like conditions on the interconnection matrix become more stringent. We also explore the stability of large-scale, time-varying interconnections of strictly positive real systems. We determine a condition that guarantees the existence of a Lyapunov function for the interconnected system.",

author = "Griggs, {Wynita M.} and Sajja, {S. Shravan K.} and Anderson, {Brian D.O.} and Shorten, {Robert N.}",

year = "2012",

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language = "English",

isbn = "9781457710957",

series = "Proceedings of the American Control Conference (ACC)",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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note = "2012 American Control Conference, ACC 2012 ; Conference date: 27-06-2012 Through 29-06-2012",

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Griggs, WM, Sajja, SSK, Anderson, BDO & Shorten, RN 2012, Extending small gain and passivity theory for large-scale system interconnections. in 2012 American Control Conference (ACC). Proceedings of the American Control Conference (ACC), Institute of Electrical and Electronics Engineers Inc., Montreal, QC, Canada, pp. 6376-6381, 2012 American Control Conference, ACC 2012, Montreal, QC, Canada, 27/06/12. https://doi.org/10.1109/acc.2012.6315476

Extending small gain and passivity theory for large-scale system interconnections. / Griggs, Wynita M.; Sajja, S. Shravan K.; Anderson, Brian D.O. et al.
2012 American Control Conference (ACC). Montreal, QC, Canada: Institute of Electrical and Electronics Engineers Inc., 2012. p. 6376-6381 (Proceedings of the American Control Conference (ACC)).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - Extending small gain and passivity theory for large-scale system interconnections

AU - Griggs, Wynita M.

AU - Sajja, S. Shravan K.

AU - Anderson, Brian D.O.

AU - Shorten, Robert N.

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N2 - In this paper, we use classical Nyquist arguments to derive stability results for large-scale interconnections of mixed linear, time-invariant (LTI) systems. We compare our results with P. J. Moylan and D. J. Hill, Stability criteria for large-scale systems, IEEE Transactions on Automatic Control, vol. 23, no. 2, 1978, pp. 143-149. Our results suggest that, if one relaxes the assumptions on the subsystems in an interconnection from assumptions of passivity or small gain to assumptions of mixedness, then the Moylan- and Hill-like conditions on the interconnection matrix become more stringent. We also explore the stability of large-scale, time-varying interconnections of strictly positive real systems. We determine a condition that guarantees the existence of a Lyapunov function for the interconnected system.

AB - In this paper, we use classical Nyquist arguments to derive stability results for large-scale interconnections of mixed linear, time-invariant (LTI) systems. We compare our results with P. J. Moylan and D. J. Hill, Stability criteria for large-scale systems, IEEE Transactions on Automatic Control, vol. 23, no. 2, 1978, pp. 143-149. Our results suggest that, if one relaxes the assumptions on the subsystems in an interconnection from assumptions of passivity or small gain to assumptions of mixedness, then the Moylan- and Hill-like conditions on the interconnection matrix become more stringent. We also explore the stability of large-scale, time-varying interconnections of strictly positive real systems. We determine a condition that guarantees the existence of a Lyapunov function for the interconnected system.

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M3 - Conference contribution

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T3 - Proceedings of the American Control Conference (ACC)

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BT - 2012 American Control Conference (ACC)

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ER -

Extending small gain and passivity theory for large-scale system interconnections

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