Lyapunov formulation of the large-scale, ISS cyclic-small-gain theorem: The discrete-time case

Tengfei Liu; David J. Hill; Zhong Ping Jiang

doi:10.1016/j.sysconle.2011.11.002

Lyapunov formulation of the large-scale, ISS cyclic-small-gain theorem: The discrete-time case

Tengfei Liu, David J. Hill, Zhong Ping Jiang

Research output: Contribution to journal › Article › Research › peer-review

26 Citations (Scopus)

Abstract

This paper presents a Lyapunov formulation of the cyclic-small-gain theorem for dynamical networks composed of discrete-time input-to-state stable (ISS) subsystems. ISS-Lyapunov functions for dynamical networks satisfying the cyclic-small-gain condition are constructed from the ISS-Lyapunov functions of the subsystems.

Original language	English
Pages (from-to)	266-272
Number of pages	7
Journal	Systems and Control Letters
Volume	61
Issue number	1
DOIs	https://doi.org/10.1016/j.sysconle.2011.11.002
Publication status	Published - Jan 2012
Externally published	Yes

Keywords

Discrete-time
Dynamical networks
Input-to-state stability (ISS)
Lyapunov functions
Small-gain

Access to Document

10.1016/j.sysconle.2011.11.002

Cite this

@article{5e8b7c1ab2f34ad5aabafdb0ea4a8cf9,

title = "Lyapunov formulation of the large-scale, ISS cyclic-small-gain theorem: The discrete-time case",

abstract = "This paper presents a Lyapunov formulation of the cyclic-small-gain theorem for dynamical networks composed of discrete-time input-to-state stable (ISS) subsystems. ISS-Lyapunov functions for dynamical networks satisfying the cyclic-small-gain condition are constructed from the ISS-Lyapunov functions of the subsystems.",

keywords = "Discrete-time, Dynamical networks, Input-to-state stability (ISS), Lyapunov functions, Small-gain",

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

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 . ",

year = "2012",

month = jan,

doi = "10.1016/j.sysconle.2011.11.002",

language = "English",

volume = "61",

pages = "266--272",

journal = "Systems and Control Letters",

issn = "0167-6911",

publisher = "Elsevier",

number = "1",

}

TY - JOUR

T1 - Lyapunov formulation of the large-scale, ISS cyclic-small-gain theorem

T2 - The discrete-time case

AU - Liu, Tengfei

AU - Hill, David J.

AU - Jiang, Zhong Ping

N1 - 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 .

PY - 2012/1

Y1 - 2012/1

N2 - This paper presents a Lyapunov formulation of the cyclic-small-gain theorem for dynamical networks composed of discrete-time input-to-state stable (ISS) subsystems. ISS-Lyapunov functions for dynamical networks satisfying the cyclic-small-gain condition are constructed from the ISS-Lyapunov functions of the subsystems.

AB - This paper presents a Lyapunov formulation of the cyclic-small-gain theorem for dynamical networks composed of discrete-time input-to-state stable (ISS) subsystems. ISS-Lyapunov functions for dynamical networks satisfying the cyclic-small-gain condition are constructed from the ISS-Lyapunov functions of the subsystems.

KW - Discrete-time

KW - Dynamical networks

KW - Input-to-state stability (ISS)

KW - Lyapunov functions

KW - Small-gain

UR - http://www.scopus.com/inward/record.url?scp=83055168393&partnerID=8YFLogxK

U2 - 10.1016/j.sysconle.2011.11.002

DO - 10.1016/j.sysconle.2011.11.002

M3 - Article

AN - SCOPUS:83055168393

SN - 0167-6911

VL - 61

SP - 266

EP - 272

JO - Systems and Control Letters

JF - Systems and Control Letters

IS - 1

ER -

Lyapunov formulation of the large-scale, ISS cyclic-small-gain theorem: The discrete-time case

Abstract

Keywords

Access to Document

Other files and links

Cite this