On infinity norms as Lyapunov functions : alternative necessary and sufficient conditions

M. Lazar

doi:10.1109/CDC.2010.5717266

On infinity norms as Lyapunov functions : alternative necessary and sufficient conditions

M. Lazar

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

40 Citations (Scopus)

722 Downloads (Pure)

Abstract

This paper considers the synthesis of infinity norm Lyapunov functions for discrete-time linear systems. A proper conic partition of the state-space is employed to construct a finite set of linear inequalities in the elements of the Lyapunov weight matrix. Under typical assumptions, it is proven that the feasibility of the derived set of linear inequalities is equivalent with the existence of an infinity norm Lyapunov function. Furthermore, it is shown that the developed solution extends naturally to several relevant classes of discrete-time nonlinear systems.

Original language	English
Title of host publication	Proceedings of the 49th IEEE Conference on Decision and Control (CDC), 15-17 December 2010, Atlanta, Georgia
Place of Publication	Piscataway
Publisher	Institute of Electrical and Electronics Engineers
Pages	5936-5942
ISBN (Print)	978-1-4244-7745-6
DOIs	https://doi.org/10.1109/CDC.2010.5717266
Publication status	Published - 2010

Access to Document

10.1109/CDC.2010.5717266

Metis245052Final published version, 205 KB

Cite this

@inproceedings{669975b1dedb447d932d35c8e73daeff,

title = "On infinity norms as Lyapunov functions : alternative necessary and sufficient conditions",

abstract = "This paper considers the synthesis of infinity norm Lyapunov functions for discrete-time linear systems. A proper conic partition of the state-space is employed to construct a finite set of linear inequalities in the elements of the Lyapunov weight matrix. Under typical assumptions, it is proven that the feasibility of the derived set of linear inequalities is equivalent with the existence of an infinity norm Lyapunov function. Furthermore, it is shown that the developed solution extends naturally to several relevant classes of discrete-time nonlinear systems.",

author = "M. Lazar",

year = "2010",

doi = "10.1109/CDC.2010.5717266",

language = "English",

isbn = "978-1-4244-7745-6",

pages = "5936--5942",

booktitle = "Proceedings of the 49th IEEE Conference on Decision and Control (CDC), 15-17 December 2010, Atlanta, Georgia",

publisher = "Institute of Electrical and Electronics Engineers",

address = "United States",

}

On infinity norms as Lyapunov functions : alternative necessary and sufficient conditions. / Lazar, M.
Proceedings of the 49th IEEE Conference on Decision and Control (CDC), 15-17 December 2010, Atlanta, Georgia. Piscataway: Institute of Electrical and Electronics Engineers, 2010. p. 5936-5942.

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

TY - GEN

T1 - On infinity norms as Lyapunov functions : alternative necessary and sufficient conditions

AU - Lazar, M.

PY - 2010

Y1 - 2010

N2 - This paper considers the synthesis of infinity norm Lyapunov functions for discrete-time linear systems. A proper conic partition of the state-space is employed to construct a finite set of linear inequalities in the elements of the Lyapunov weight matrix. Under typical assumptions, it is proven that the feasibility of the derived set of linear inequalities is equivalent with the existence of an infinity norm Lyapunov function. Furthermore, it is shown that the developed solution extends naturally to several relevant classes of discrete-time nonlinear systems.

AB - This paper considers the synthesis of infinity norm Lyapunov functions for discrete-time linear systems. A proper conic partition of the state-space is employed to construct a finite set of linear inequalities in the elements of the Lyapunov weight matrix. Under typical assumptions, it is proven that the feasibility of the derived set of linear inequalities is equivalent with the existence of an infinity norm Lyapunov function. Furthermore, it is shown that the developed solution extends naturally to several relevant classes of discrete-time nonlinear systems.

U2 - 10.1109/CDC.2010.5717266

DO - 10.1109/CDC.2010.5717266

M3 - Conference contribution

SN - 978-1-4244-7745-6

SP - 5936

EP - 5942

BT - Proceedings of the 49th IEEE Conference on Decision and Control (CDC), 15-17 December 2010, Atlanta, Georgia

PB - Institute of Electrical and Electronics Engineers

CY - Piscataway

ER -

On infinity norms as Lyapunov functions : alternative necessary and sufficient conditions

Abstract

Access to Document

Fingerprint

Cite this