Feedback stabilization via rational control Lyapunov functions

A.I. Doban; M. Lazar

doi:10.1109/CDC.2015.7402366

Feedback stabilization via rational control Lyapunov functions

A.I. Doban, M. Lazar

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

5 Citations (Scopus)

2 Downloads (Pure)

Abstract

We provide a procedure which generates a rational control Lyapunov function and a polynomial stabilizer for nonlinear systems described by analytic functions satisfying some regularity conditions. Furthermore, an improved estimate of the domain of attraction of the closed-loop system can be computed by means of previously introduced rational Lypunov functions. For polynomial systems, we indicate that the existence of a polynomial feedback stabilizer is guaranteed by the existence of a rational control Lyapunov function. We illustrate the proposed procedure for the stabilization of the population co-existence equilibrium of a predator-prey model describing tumor dynamics.

Original language	English
Title of host publication	2015 54th IEEE Conference on Decision and Control (CDC), 15-18 December 2015, Osaka, Japan
Place of Publication	Piscataway
Publisher	Institute of Electrical and Electronics Engineers
Pages	1148-1153
ISBN (Print)	978-1-4799-7884-7
DOIs	https://doi.org/10.1109/CDC.2015.7402366
Publication status	Published - 2015
Event	54th IEEE Conference on Decision and Control (CDC 2015) - "Osaka International Convention Center", Osaka, Japan Duration: 15 Dec 2015 → 18 Dec 2015 Conference number: 54 http://www.cdc2015.ctrl.titech.ac.jp/

Conference

Conference	54th IEEE Conference on Decision and Control (CDC 2015)
Abbreviated title	CDC 2015
Country/Territory	Japan
City	Osaka
Period	15/12/15 → 18/12/15
Internet address	http://www.cdc2015.ctrl.titech.ac.jp/

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10.1109/CDC.2015.7402366

Cite this

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title = "Feedback stabilization via rational control Lyapunov functions",

abstract = "We provide a procedure which generates a rational control Lyapunov function and a polynomial stabilizer for nonlinear systems described by analytic functions satisfying some regularity conditions. Furthermore, an improved estimate of the domain of attraction of the closed-loop system can be computed by means of previously introduced rational Lypunov functions. For polynomial systems, we indicate that the existence of a polynomial feedback stabilizer is guaranteed by the existence of a rational control Lyapunov function. We illustrate the proposed procedure for the stabilization of the population co-existence equilibrium of a predator-prey model describing tumor dynamics.",

author = "A.I. Doban and M. Lazar",

year = "2015",

doi = "10.1109/CDC.2015.7402366",

language = "English",

isbn = "978-1-4799-7884-7",

pages = "1148--1153",

booktitle = "2015 54th IEEE Conference on Decision and Control (CDC), 15-18 December 2015, Osaka, Japan",

publisher = "Institute of Electrical and Electronics Engineers",

address = "United States",

note = "54th IEEE Conference on Decision and Control (CDC 2015), CDC 2015 ; Conference date: 15-12-2015 Through 18-12-2015",

url = "http://www.cdc2015.ctrl.titech.ac.jp/",

}

Doban, AI & Lazar, M 2015, Feedback stabilization via rational control Lyapunov functions. in 2015 54th IEEE Conference on Decision and Control (CDC), 15-18 December 2015, Osaka, Japan. Institute of Electrical and Electronics Engineers, Piscataway, pp. 1148-1153, 54th IEEE Conference on Decision and Control (CDC 2015), Osaka, Japan, 15/12/15. https://doi.org/10.1109/CDC.2015.7402366

Feedback stabilization via rational control Lyapunov functions. / Doban, A.I.; Lazar, M.
2015 54th IEEE Conference on Decision and Control (CDC), 15-18 December 2015, Osaka, Japan. Piscataway: Institute of Electrical and Electronics Engineers, 2015. p. 1148-1153.

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

TY - GEN

T1 - Feedback stabilization via rational control Lyapunov functions

AU - Doban, A.I.

AU - Lazar, M.

N1 - Conference code: 54

PY - 2015

Y1 - 2015

N2 - We provide a procedure which generates a rational control Lyapunov function and a polynomial stabilizer for nonlinear systems described by analytic functions satisfying some regularity conditions. Furthermore, an improved estimate of the domain of attraction of the closed-loop system can be computed by means of previously introduced rational Lypunov functions. For polynomial systems, we indicate that the existence of a polynomial feedback stabilizer is guaranteed by the existence of a rational control Lyapunov function. We illustrate the proposed procedure for the stabilization of the population co-existence equilibrium of a predator-prey model describing tumor dynamics.

AB - We provide a procedure which generates a rational control Lyapunov function and a polynomial stabilizer for nonlinear systems described by analytic functions satisfying some regularity conditions. Furthermore, an improved estimate of the domain of attraction of the closed-loop system can be computed by means of previously introduced rational Lypunov functions. For polynomial systems, we indicate that the existence of a polynomial feedback stabilizer is guaranteed by the existence of a rational control Lyapunov function. We illustrate the proposed procedure for the stabilization of the population co-existence equilibrium of a predator-prey model describing tumor dynamics.

U2 - 10.1109/CDC.2015.7402366

DO - 10.1109/CDC.2015.7402366

M3 - Conference contribution

SN - 978-1-4799-7884-7

SP - 1148

EP - 1153

BT - 2015 54th IEEE Conference on Decision and Control (CDC), 15-18 December 2015, Osaka, Japan

PB - Institute of Electrical and Electronics Engineers

CY - Piscataway

T2 - 54th IEEE Conference on Decision and Control (CDC 2015)

Y2 - 15 December 2015 through 18 December 2015

ER -

Feedback stabilization via rational control Lyapunov functions

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