On the stabilizability of multiple integrators by means of bounded feedback controls

Hector J. Sussmann; Yudi Yang

On the stabilizability of multiple integrators by means of bounded feedback controls

Hector J. Sussmann, Yudi Yang

School of Arts and Sciences, Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

138 Scopus citations

Abstract

It is known that a linear x= Ax + Bu can be stabilized by means of a smooth bounded control if and only if it has no eigenvalues with positive real part, and all the uncontrollable modes have a negative real part. Here, the authors investigate, for single-input systems, the question of whether such systems can be stabilized by means of a feedback u = σ(h(x)), where h is linear and σ(s) is a saturation function such as sign(s) min(|s|,1). A stabilizing feedback of this particular form exists if A has no multiple eigenvalues, and also in some other special cases such as the double integrator. It is shown that for the multiple integrator of order n, with n ≥ 3, no saturation of a linear feedback can be globally stabilizing.

Original language	English (US)
Title of host publication	Proceedings of the IEEE Conference on Decision and Control
Publisher	Publ by IEEE
Pages	70-72
Number of pages	3
ISBN (Print)	0780304500
State	Published - Jan 1 1992
Event	Proceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3) - Brighton, Engl Duration: Dec 11 1991 → Dec 13 1991

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0191-2216

Other

Other	Proceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3)
City	Brighton, Engl
Period	12/11/91 → 12/13/91

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Access to Document

Fingerprint Dive into the research topics of 'On the stabilizability of multiple integrators by means of bounded feedback controls'. Together they form a unique fingerprint.

Cite this

@inproceedings{6826cb210e1242c6875c3b3a294c5018,

title = "On the stabilizability of multiple integrators by means of bounded feedback controls",

abstract = "It is known that a linear x= Ax + Bu can be stabilized by means of a smooth bounded control if and only if it has no eigenvalues with positive real part, and all the uncontrollable modes have a negative real part. Here, the authors investigate, for single-input systems, the question of whether such systems can be stabilized by means of a feedback u = σ(h(x)), where h is linear and σ(s) is a saturation function such as sign(s) min(|s|,1). A stabilizing feedback of this particular form exists if A has no multiple eigenvalues, and also in some other special cases such as the double integrator. It is shown that for the multiple integrator of order n, with n ≥ 3, no saturation of a linear feedback can be globally stabilizing.",

author = "Sussmann, {Hector J.} and Yudi Yang",

year = "1992",

month = jan,

day = "1",

language = "English (US)",

isbn = "0780304500",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Publ by IEEE",

pages = "70--72",

booktitle = "Proceedings of the IEEE Conference on Decision and Control",

note = "Proceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3) ; Conference date: 11-12-1991 Through 13-12-1991",

}

TY - GEN

T1 - On the stabilizability of multiple integrators by means of bounded feedback controls

AU - Sussmann, Hector J.

AU - Yang, Yudi

PY - 1992/1/1

Y1 - 1992/1/1

N2 - It is known that a linear x= Ax + Bu can be stabilized by means of a smooth bounded control if and only if it has no eigenvalues with positive real part, and all the uncontrollable modes have a negative real part. Here, the authors investigate, for single-input systems, the question of whether such systems can be stabilized by means of a feedback u = σ(h(x)), where h is linear and σ(s) is a saturation function such as sign(s) min(|s|,1). A stabilizing feedback of this particular form exists if A has no multiple eigenvalues, and also in some other special cases such as the double integrator. It is shown that for the multiple integrator of order n, with n ≥ 3, no saturation of a linear feedback can be globally stabilizing.

AB - It is known that a linear x= Ax + Bu can be stabilized by means of a smooth bounded control if and only if it has no eigenvalues with positive real part, and all the uncontrollable modes have a negative real part. Here, the authors investigate, for single-input systems, the question of whether such systems can be stabilized by means of a feedback u = σ(h(x)), where h is linear and σ(s) is a saturation function such as sign(s) min(|s|,1). A stabilizing feedback of this particular form exists if A has no multiple eigenvalues, and also in some other special cases such as the double integrator. It is shown that for the multiple integrator of order n, with n ≥ 3, no saturation of a linear feedback can be globally stabilizing.

UR - http://www.scopus.com/inward/record.url?scp=0026673743&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026673743&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0026673743

SN - 0780304500

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 70

EP - 72

BT - Proceedings of the IEEE Conference on Decision and Control

PB - Publ by IEEE

T2 - Proceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3)

Y2 - 11 December 1991 through 13 December 1991

ER -