Explicit Form of Lyapunov Functions for a Class of Nonlinear Feedback Systems Augmented with Observers

Anton Shiriaev; Rolf Johansson; Anders Robertsson

Explicit Form of Lyapunov Functions for a Class of Nonlinear Feedback Systems Augmented with Observers

Anton Shiriaev, Rolf Johansson, Anders Robertsson

Department of Automatic Control

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

Abstract

The paper suggests conditions for presence of quadratic Lyapunov functions for nonlinear observer based feedback systems with an 'input nonlinearity' in the feedback path. Provided that the system using state feedback satisfies the Circle Criterion (i.e., when all states can be measured), we show that the extended system with only output feedback control from a (full state) Luenberger-type observer also can apply to the Circle Criterion. As a consequence, we state a separation principle for a class of feedback systems with an 'input nonlinearity.' When only local stability results can be stated,
our method provides an estimate of the region of attraction.

Original language	English
Title of host publication	Preprints 7th IFAC Symp. Nonlinear Control Systems (NOLCOS 2007)
Publication status	Published - 2007
Event	7th IFAC Symposium on Nonlinear Control Systems, 2007 - Pretoria, South Africa Duration: 2007 Aug 22 → 2007 Aug 24 Conference number: 7

Conference

Conference	7th IFAC Symposium on Nonlinear Control Systems, 2007
Abbreviated title	NOLCOS'07
Country/Territory	South Africa
City	Pretoria
Period	2007/08/22 → 2007/08/24

Subject classification (UKÄ)

Control Engineering

Active Control 2007-2009
Johansson, R. (PI)
2007/01/01 → 2009/12/31
Project: Research

Cite this

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title = "Explicit Form of Lyapunov Functions for a Class of Nonlinear Feedback Systems Augmented with Observers",

abstract = "The paper suggests conditions for presence of quadratic Lyapunov functions for nonlinear observer based feedback systems with an 'input nonlinearity' in the feedback path. Provided that the system using state feedback satisfies the Circle Criterion (i.e., when all states can be measured), we show that the extended system with only output feedback control from a (full state) Luenberger-type observer also can apply to the Circle Criterion. As a consequence, we state a separation principle for a class of feedback systems with an 'input nonlinearity.' When only local stability results can be stated, our method provides an estimate of the region of attraction.",

author = "Anton Shiriaev and Rolf Johansson and Anders Robertsson",

year = "2007",

language = "English",

booktitle = "Preprints 7th IFAC Symp. Nonlinear Control Systems (NOLCOS 2007)",

note = "7th IFAC Symposium on Nonlinear Control Systems, 2007, NOLCOS'07 ; Conference date: 22-08-2007 Through 24-08-2007",

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TY - GEN

T1 - Explicit Form of Lyapunov Functions for a Class of Nonlinear Feedback Systems Augmented with Observers

AU - Shiriaev, Anton

AU - Johansson, Rolf

AU - Robertsson, Anders

N1 - Conference code: 7

PY - 2007

Y1 - 2007

N2 - The paper suggests conditions for presence of quadratic Lyapunov functions for nonlinear observer based feedback systems with an 'input nonlinearity' in the feedback path. Provided that the system using state feedback satisfies the Circle Criterion (i.e., when all states can be measured), we show that the extended system with only output feedback control from a (full state) Luenberger-type observer also can apply to the Circle Criterion. As a consequence, we state a separation principle for a class of feedback systems with an 'input nonlinearity.' When only local stability results can be stated, our method provides an estimate of the region of attraction.

AB - The paper suggests conditions for presence of quadratic Lyapunov functions for nonlinear observer based feedback systems with an 'input nonlinearity' in the feedback path. Provided that the system using state feedback satisfies the Circle Criterion (i.e., when all states can be measured), we show that the extended system with only output feedback control from a (full state) Luenberger-type observer also can apply to the Circle Criterion. As a consequence, we state a separation principle for a class of feedback systems with an 'input nonlinearity.' When only local stability results can be stated, our method provides an estimate of the region of attraction.

M3 - Paper in conference proceeding

BT - Preprints 7th IFAC Symp. Nonlinear Control Systems (NOLCOS 2007)

T2 - 7th IFAC Symposium on Nonlinear Control Systems, 2007

Y2 - 22 August 2007 through 24 August 2007

ER -

Explicit Form of Lyapunov Functions for a Class of Nonlinear Feedback Systems Augmented with Observers

Abstract

Conference

Subject classification (UKÄ)

Fingerprint

Projects

Active Control 2007-2009

Cite this