Achieving nonvanishing stability regions with high-gain cheap control using H∞ techniques: The second order case

Gregory J. Toussaint; Tamer Basar

Achieving nonvanishing stability regions with high-gain cheap control using H^∞ techniques: The second order case

Gregory J. Toussaint
, Tamer Basar

Research output: Contribution to journal › Conference article › peer-review

Abstract

We use asymptotically optimal H^∞ design techniques to develop a high-gain linear feedback controller to stabilize a class of nonlinear systems. We determine conditions on the design parameters to guarantee that the high-gain control does not cause the stability region to vanish. Our approach uses a Lyapunov function to derive a sufficient condition to maintain the stability region for a second-order system when we know a bound on the nonlinear terms. A simulation confirms the results.

Original language	English (US)
Pages (from-to)	1279-1283
Number of pages	5
Journal	Proceedings of the American Control Conference
Volume	2
State	Published - 1999
Event	Proceedings of the 1999 American Control Conference (99ACC) - San Diego, CA, USA Duration: Jun 2 1999 → Jun 4 1999

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Electrical and Electronic Engineering

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title = "Achieving nonvanishing stability regions with high-gain cheap control using H∞ techniques: The second order case",

abstract = "We use asymptotically optimal H∞ design techniques to develop a high-gain linear feedback controller to stabilize a class of nonlinear systems. We determine conditions on the design parameters to guarantee that the high-gain control does not cause the stability region to vanish. Our approach uses a Lyapunov function to derive a sufficient condition to maintain the stability region for a second-order system when we know a bound on the nonlinear terms. A simulation confirms the results.",

author = "Toussaint, \{Gregory J.\} and Tamer Basar",

note = "We wish to acknowledge discussions with and contributions of Scott Splater, Zigang Pan, and Petar V. Kokotovi{\'c} at the earlier stages of this research. The anonymous reviewers also provided several valuable suggestions to improve the final document. This research was supported in part by the US Department of Energy under Grant DE-FG-02-97-ER-13939.; Proceedings of the 1999 American Control Conference (99ACC) ; Conference date: 02-06-1999 Through 04-06-1999",

year = "1999",

language = "English (US)",

volume = "2",

pages = "1279--1283",

journal = "Proceedings of the American Control Conference",

issn = "0743-1619",

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TY - JOUR

T1 - Achieving nonvanishing stability regions with high-gain cheap control using H∞ techniques

T2 - Proceedings of the 1999 American Control Conference (99ACC)

AU - Toussaint, Gregory J.

AU - Basar, Tamer

N1 - We wish to acknowledge discussions with and contributions of Scott Splater, Zigang Pan, and Petar V. Kokotović at the earlier stages of this research. The anonymous reviewers also provided several valuable suggestions to improve the final document. This research was supported in part by the US Department of Energy under Grant DE-FG-02-97-ER-13939.

PY - 1999

Y1 - 1999

N2 - We use asymptotically optimal H∞ design techniques to develop a high-gain linear feedback controller to stabilize a class of nonlinear systems. We determine conditions on the design parameters to guarantee that the high-gain control does not cause the stability region to vanish. Our approach uses a Lyapunov function to derive a sufficient condition to maintain the stability region for a second-order system when we know a bound on the nonlinear terms. A simulation confirms the results.

AB - We use asymptotically optimal H∞ design techniques to develop a high-gain linear feedback controller to stabilize a class of nonlinear systems. We determine conditions on the design parameters to guarantee that the high-gain control does not cause the stability region to vanish. Our approach uses a Lyapunov function to derive a sufficient condition to maintain the stability region for a second-order system when we know a bound on the nonlinear terms. A simulation confirms the results.

UR - https://www.scopus.com/pages/publications/0033284190

UR - https://www.scopus.com/pages/publications/0033284190#tab=citedBy

M3 - Conference article

AN - SCOPUS:0033284190

SN - 0743-1619

VL - 2

SP - 1279

EP - 1283

JO - Proceedings of the American Control Conference

JF - Proceedings of the American Control Conference

Y2 - 2 June 1999 through 4 June 1999

ER -

Achieving nonvanishing stability regions with high-gain cheap control using H^∞ techniques: The second order case

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