On infinity norms as Lyapunov functions for continuous-time dynamical systems

Mircea Lazar; Alina I. Doban

doi:10.1109/CDC.2011.6161163

On infinity norms as Lyapunov functions for continuous-time dynamical systems

Mircea Lazar
, Alina I. Doban

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

12 Citations (Scopus)

Abstract

This paper considers the synthesis of polyhedral Lyapunov functions for continuous-time dynamical 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. For dynamics described by linear and polytopic differential inclusions, it is proven that the feasibility of the derived set of linear inequalities is necessary and sufficient for the existence of an infinity norm Lyapunov function. Furthermore, it is shown that the developed solution naturally applies to relevant classes of continuous-time nonlinear systems. An extension to non-symmetric polyhedral Lyapunov functions is also presented.

Original language	English
Title of host publication	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Place of Publication	Piscataway
Publisher	Institute of Electrical and Electronics Engineers
Pages	7567-7572
Number of pages	6
ISBN (Print)	9781612848006
DOIs	https://doi.org/10.1109/CDC.2011.6161163
Publication status	Published - 1 Dec 2011
Event	50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC 2011) - Hilton Orlando Bonnet Creek, Orlando, United States Duration: 12 Dec 2011 → 15 Dec 2011 Conference number: 50 http://www.ieeecss.org/CAB/conferences/cdcecc2011/

Conference

Conference	50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC 2011)
Abbreviated title	CDC-ECC 2011
Country/Territory	United States
City	Orlando
Period	12/12/11 → 15/12/11
Other	50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Internet address	http://www.ieeecss.org/CAB/conferences/cdcecc2011/

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10.1109/CDC.2011.6161163

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title = "On infinity norms as Lyapunov functions for continuous-time dynamical systems",

abstract = "This paper considers the synthesis of polyhedral Lyapunov functions for continuous-time dynamical 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. For dynamics described by linear and polytopic differential inclusions, it is proven that the feasibility of the derived set of linear inequalities is necessary and sufficient for the existence of an infinity norm Lyapunov function. Furthermore, it is shown that the developed solution naturally applies to relevant classes of continuous-time nonlinear systems. An extension to non-symmetric polyhedral Lyapunov functions is also presented.",

author = "Mircea Lazar and Doban, \{Alina I.\}",

year = "2011",

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doi = "10.1109/CDC.2011.6161163",

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booktitle = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011",

publisher = "Institute of Electrical and Electronics Engineers",

address = "United States",

note = "50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC 2011), CDC-ECC 2011 ; Conference date: 12-12-2011 Through 15-12-2011",

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Lazar, M & Doban, AI 2011, On infinity norms as Lyapunov functions for continuous-time dynamical systems. in 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011., 6161163, Institute of Electrical and Electronics Engineers, Piscataway, pp. 7567-7572, 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC 2011), Orlando, Florida, United States, 12/12/11. https://doi.org/10.1109/CDC.2011.6161163

On infinity norms as Lyapunov functions for continuous-time dynamical systems. / Lazar, Mircea; Doban, Alina I.
2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. Piscataway: Institute of Electrical and Electronics Engineers, 2011. p. 7567-7572 6161163.

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

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AU - Doban, Alina I.

N1 - Conference code: 50

PY - 2011/12/1

Y1 - 2011/12/1

N2 - This paper considers the synthesis of polyhedral Lyapunov functions for continuous-time dynamical 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. For dynamics described by linear and polytopic differential inclusions, it is proven that the feasibility of the derived set of linear inequalities is necessary and sufficient for the existence of an infinity norm Lyapunov function. Furthermore, it is shown that the developed solution naturally applies to relevant classes of continuous-time nonlinear systems. An extension to non-symmetric polyhedral Lyapunov functions is also presented.

AB - This paper considers the synthesis of polyhedral Lyapunov functions for continuous-time dynamical 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. For dynamics described by linear and polytopic differential inclusions, it is proven that the feasibility of the derived set of linear inequalities is necessary and sufficient for the existence of an infinity norm Lyapunov function. Furthermore, it is shown that the developed solution naturally applies to relevant classes of continuous-time nonlinear systems. An extension to non-symmetric polyhedral Lyapunov functions is also presented.

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U2 - 10.1109/CDC.2011.6161163

DO - 10.1109/CDC.2011.6161163

M3 - Conference contribution

AN - SCOPUS:84860669831

SN - 9781612848006

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EP - 7572

BT - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011

PB - Institute of Electrical and Electronics Engineers

CY - Piscataway

T2 - 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC 2011)

Y2 - 12 December 2011 through 15 December 2011

ER -

On infinity norms as Lyapunov functions for continuous-time dynamical systems

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