Lyapunov-ISS cyclic-small-gain in hybrid dynamical networks

Tengfei Liu; Zhong-Ping Jiang; David J. Hill

doi:10.3182/20100901-3-IT-2016.00016

Lyapunov-ISS cyclic-small-gain in hybrid dynamical networks

Tengfei Liu, Zhong-Ping Jiang, David J. Hill

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

4 Citations (Scopus)

Abstract

This paper develops a cyclic-small-gain theorem for hybrid dynamical networks composed of continuous-time and discrete-time input-to-state stable (ISS) subsystems. The main result is achieved in two steps: a) A hybrid dynamical network composed of ISS subsystems with interconnection gains less than the identity is ISS; b) Any hybrid dynamical networks satisfying the cyclic-small-gain condition can be transformed into networks with interconnection gains less than the identity. The sampling times of the discrete-time subsystems are independent of the states, which makes this result different from several of the existing results.

Original language	English
Title of host publication	8th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2010
Publisher	Elsevier - International Federation of Automatic Control (IFAC)
Pages	813-818
Number of pages	6
Edition	14
ISBN (Print)	9783902661807
DOIs	https://doi.org/10.3182/20100901-3-IT-2016.00016
Publication status	Published - 2010
Externally published	Yes
Event	Symposium on Nonlinear Control Systems 2010 - Bologna, Italy Duration: 1 Sept 2010 → 1 Sept 2010 Conference number: 8th https://www.sciencedirect.com/journal/ifac-proceedings-volumes/vol/43/issue/14

Publication series

Name	IFAC Proceedings Volumes (IFAC-PapersOnline)
Number	14
Volume	43
ISSN (Print)	1474-6670

Conference

Conference	Symposium on Nonlinear Control Systems 2010
Country/Territory	Italy
City	Bologna
Period	1/09/10 → 1/09/10
Internet address	https://www.sciencedirect.com/journal/ifac-proceedings-volumes/vol/43/issue/14

Keywords

Cyclic-small-gain
Hybrid systems
Lyapunov formulation

Access to Document

10.3182/20100901-3-IT-2016.00016

Cite this

Liu, T., Jiang, Z.-P., & Hill, D. J. (2010). Lyapunov-ISS cyclic-small-gain in hybrid dynamical networks. In 8th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2010 (14 ed., pp. 813-818). (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 43, No. 14). Elsevier - International Federation of Automatic Control (IFAC). https://doi.org/10.3182/20100901-3-IT-2016.00016

@inproceedings{5d996743085b4141a7c5345c3da224c8,

title = "Lyapunov-ISS cyclic-small-gain in hybrid dynamical networks",

abstract = "This paper develops a cyclic-small-gain theorem for hybrid dynamical networks composed of continuous-time and discrete-time input-to-state stable (ISS) subsystems. The main result is achieved in two steps: a) A hybrid dynamical network composed of ISS subsystems with interconnection gains less than the identity is ISS; b) Any hybrid dynamical networks satisfying the cyclic-small-gain condition can be transformed into networks with interconnection gains less than the identity. The sampling times of the discrete-time subsystems are independent of the states, which makes this result different from several of the existing results.",

keywords = "Cyclic-small-gain, Hybrid systems, Lyapunov formulation",

author = "Tengfei Liu and Zhong-Ping Jiang and Hill, \{David J.\}",

note = "Funding Information: ★ This research was supported under the Australian Research Councils Discovery funding scheme (project number: FF0455875), in part by a seed grant from NYU and POLY, and by NSF grant DMS-0906659.; Symposium on Nonlinear Control Systems 2010 ; Conference date: 01-09-2010 Through 01-09-2010",

year = "2010",

doi = "10.3182/20100901-3-IT-2016.00016",

language = "English",

isbn = "9783902661807",

series = "IFAC Proceedings Volumes (IFAC-PapersOnline)",

publisher = "Elsevier - International Federation of Automatic Control (IFAC)",

number = "14",

pages = "813--818",

booktitle = "8th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2010",

edition = "14",

url = "https://www.sciencedirect.com/journal/ifac-proceedings-volumes/vol/43/issue/14",

}

Liu, T, Jiang, Z-P & Hill, DJ 2010, Lyapunov-ISS cyclic-small-gain in hybrid dynamical networks. in 8th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2010. 14 edn, IFAC Proceedings Volumes (IFAC-PapersOnline), no. 14, vol. 43, Elsevier - International Federation of Automatic Control (IFAC), pp. 813-818, Symposium on Nonlinear Control Systems 2010, Bologna, Italy, 1/09/10. https://doi.org/10.3182/20100901-3-IT-2016.00016

Lyapunov-ISS cyclic-small-gain in hybrid dynamical networks. / Liu, Tengfei; Jiang, Zhong-Ping; Hill, David J.
8th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2010. 14. ed. Elsevier - International Federation of Automatic Control (IFAC), 2010. p. 813-818 (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 43, No. 14).

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

TY - GEN

T1 - Lyapunov-ISS cyclic-small-gain in hybrid dynamical networks

AU - Liu, Tengfei

AU - Jiang, Zhong-Ping

AU - Hill, David J.

N1 - Conference code: 8th

PY - 2010

Y1 - 2010

N2 - This paper develops a cyclic-small-gain theorem for hybrid dynamical networks composed of continuous-time and discrete-time input-to-state stable (ISS) subsystems. The main result is achieved in two steps: a) A hybrid dynamical network composed of ISS subsystems with interconnection gains less than the identity is ISS; b) Any hybrid dynamical networks satisfying the cyclic-small-gain condition can be transformed into networks with interconnection gains less than the identity. The sampling times of the discrete-time subsystems are independent of the states, which makes this result different from several of the existing results.

AB - This paper develops a cyclic-small-gain theorem for hybrid dynamical networks composed of continuous-time and discrete-time input-to-state stable (ISS) subsystems. The main result is achieved in two steps: a) A hybrid dynamical network composed of ISS subsystems with interconnection gains less than the identity is ISS; b) Any hybrid dynamical networks satisfying the cyclic-small-gain condition can be transformed into networks with interconnection gains less than the identity. The sampling times of the discrete-time subsystems are independent of the states, which makes this result different from several of the existing results.

KW - Cyclic-small-gain

KW - Hybrid systems

KW - Lyapunov formulation

UR - https://www.scopus.com/pages/publications/80051735451

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DO - 10.3182/20100901-3-IT-2016.00016

M3 - Conference Paper

AN - SCOPUS:80051735451

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T3 - IFAC Proceedings Volumes (IFAC-PapersOnline)

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BT - 8th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2010

PB - Elsevier - International Federation of Automatic Control (IFAC)

T2 - Symposium on Nonlinear Control Systems 2010

Y2 - 1 September 2010 through 1 September 2010

ER -

Lyapunov-ISS cyclic-small-gain in hybrid dynamical networks

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