Nonlinear versus linear control in the absolute stabilizability of uncertain systems with structured uncertainty

Andrey V. Savkin; Ian R. Petersen

Nonlinear versus linear control in the absolute stabilizability of uncertain systems with structured uncertainty

Andrey V. Savkin^*
, Ian R. Petersen

^*Corresponding author for this work

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

17 Citations (Scopus)

Abstract

This paper considers a stabilization problem for a class of uncertain linear systems containing structured uncertainty. The uncertainties in the system are described by a certain Integral Quadratic Constraint which allows for a rich class of uncertainties including nonlinear dynamic time-varying uncertainty. The notion of stabilizability considered is that of absolute stabilizability. The main results show that the question of absolute stabilizability for the class of uncertain linear systems under consideration is equivalent to the existence of a solution to a corresponding `diagonally scaled' H^∞ control problem. A consequence of this result is the fact that absolute stabilizability via nonlinear control implies absolute stabilizability via linear control.

Original language	English
Title of host publication	Proceedings of the IEEE Conference on Decision and Control
Publisher	IEEE
Pages	172-177
Number of pages	6
Volume	1
Publication status	Published - 1993
Externally published	Yes
Event	Proceedings of the 32nd Conference on Decision and Control - San Antonio, TX, USA Duration: 15 Dec 1993 → 15 Dec 1993

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISSN (Print)	0191-2216

Conference

Conference	Proceedings of the 32nd Conference on Decision and Control
City	San Antonio, TX, USA
Period	15/12/93 → 15/12/93

Cite this

@inproceedings{9c4ed0c7f9854137932df2b7024f33b9,

title = "Nonlinear versus linear control in the absolute stabilizability of uncertain systems with structured uncertainty",

abstract = "This paper considers a stabilization problem for a class of uncertain linear systems containing structured uncertainty. The uncertainties in the system are described by a certain Integral Quadratic Constraint which allows for a rich class of uncertainties including nonlinear dynamic time-varying uncertainty. The notion of stabilizability considered is that of absolute stabilizability. The main results show that the question of absolute stabilizability for the class of uncertain linear systems under consideration is equivalent to the existence of a solution to a corresponding `diagonally scaled' H∞ control problem. A consequence of this result is the fact that absolute stabilizability via nonlinear control implies absolute stabilizability via linear control.",

author = "Savkin, \{Andrey V.\} and Petersen, \{Ian R.\}",

year = "1993",

language = "English",

volume = "1",

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

publisher = "IEEE",

pages = "172--177",

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

note = "Proceedings of the 32nd Conference on Decision and Control ; Conference date: 15-12-1993 Through 15-12-1993",

}

Savkin, AV & Petersen, IR 1993, Nonlinear versus linear control in the absolute stabilizability of uncertain systems with structured uncertainty. in Proceedings of the IEEE Conference on Decision and Control. vol. 1, Proceedings of the IEEE Conference on Decision and Control, IEEE, pp. 172-177, Proceedings of the 32nd Conference on Decision and Control, San Antonio, TX, USA, 15/12/93.

Nonlinear versus linear control in the absolute stabilizability of uncertain systems with structured uncertainty. / Savkin, Andrey V.; Petersen, Ian R.
Proceedings of the IEEE Conference on Decision and Control. Vol. 1 IEEE, 1993. p. 172-177 (Proceedings of the IEEE Conference on Decision and Control).

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

TY - GEN

T1 - Nonlinear versus linear control in the absolute stabilizability of uncertain systems with structured uncertainty

AU - Savkin, Andrey V.

AU - Petersen, Ian R.

PY - 1993

Y1 - 1993

N2 - This paper considers a stabilization problem for a class of uncertain linear systems containing structured uncertainty. The uncertainties in the system are described by a certain Integral Quadratic Constraint which allows for a rich class of uncertainties including nonlinear dynamic time-varying uncertainty. The notion of stabilizability considered is that of absolute stabilizability. The main results show that the question of absolute stabilizability for the class of uncertain linear systems under consideration is equivalent to the existence of a solution to a corresponding `diagonally scaled' H∞ control problem. A consequence of this result is the fact that absolute stabilizability via nonlinear control implies absolute stabilizability via linear control.

AB - This paper considers a stabilization problem for a class of uncertain linear systems containing structured uncertainty. The uncertainties in the system are described by a certain Integral Quadratic Constraint which allows for a rich class of uncertainties including nonlinear dynamic time-varying uncertainty. The notion of stabilizability considered is that of absolute stabilizability. The main results show that the question of absolute stabilizability for the class of uncertain linear systems under consideration is equivalent to the existence of a solution to a corresponding `diagonally scaled' H∞ control problem. A consequence of this result is the fact that absolute stabilizability via nonlinear control implies absolute stabilizability via linear control.

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M3 - Conference Paper

AN - SCOPUS:0027741538

VL - 1

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 172

EP - 177

BT - Proceedings of the IEEE Conference on Decision and Control

PB - IEEE

T2 - Proceedings of the 32nd Conference on Decision and Control

Y2 - 15 December 1993 through 15 December 1993

ER -

Nonlinear versus linear control in the absolute stabilizability of uncertain systems with structured uncertainty

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