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

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Other

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 2012
Publisher	IEEE, Institute of Electrical and Electronics Engineers
Pages	6376-6381
Number of pages	6
ISBN (Print)	9781457710957
DOIs	https://doi.org/10.1109/acc.2012.6315476
Publication status	Published - 2012
Externally published	Yes
Event	American Control Conference 2012 - Montreal, Canada Duration: 27 Jun 2012 → 29 Jun 2012 https://ieeexplore.ieee.org/xpl/conhome/6297579/proceeding (Proceedings)

Publication series

Name	Proceedings of the American Control Conference
ISSN (Print)	0743-1619

Conference

Conference	American Control Conference 2012
Abbreviated title	ACC 2012
Country/Territory	Canada
City	Montreal
Period	27/06/12 → 29/06/12
Internet address	https://ieeexplore.ieee.org/xpl/conhome/6297579/proceeding (Proceedings)

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10.1109/acc.2012.6315476

Cite this

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 2012 (pp. 6376-6381). (Proceedings of the American Control Conference). IEEE, Institute of Electrical and Electronics Engineers. 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",

doi = "10.1109/acc.2012.6315476",

language = "English",

isbn = "9781457710957",

series = "Proceedings of the American Control Conference",

publisher = "IEEE, Institute of Electrical and Electronics Engineers",

pages = "6376--6381",

booktitle = "2012 American Control Conference, ACC 2012",

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url = "https://ieeexplore.ieee.org/xpl/conhome/6297579/proceeding",

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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 2012. Proceedings of the American Control Conference, IEEE, Institute of Electrical and Electronics Engineers, pp. 6376-6381, American Control Conference 2012 , Montreal, Quebec, 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 2012. IEEE, Institute of Electrical and Electronics Engineers, 2012. p. 6376-6381 (Proceedings of the American Control Conference).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Other

TY - GEN

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.

PY - 2012

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

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