# A Globally Exponentially Convergent Immersion and Invariance Speed Observer for n--Degrees of Freedom Mechanical Systems

### Alessandro Astilfi, Romeo Ortega, Aneesh Venkatraman

#### Abstract

The problem of velocity estimation for mechanical systems is of great practical interest. Although many partial solutions have been reported in the literature the basic question of whether it is possible to design a globally convergent speed observer for general n degrees of freedom mechanical systems remains open. In this paper an affirmative answer to the question is given by proving the existence of a 3n+1--dimensional globally em exponentially convergent speed observer. Instrumental for the construction of the speed observer is the use of the Immersion and Invariance technique, in which the observer design problem is recast as a problem of rendering attractive and invariant a manifold defined in the extended state--space of the plant and the observer.

Download#### Paper Citation

#### in Harvard Style

Astilfi A., Ortega R. and Venkatraman A. (2009). **A Globally Exponentially Convergent Immersion and Invariance Speed Observer for n--Degrees of Freedom Mechanical Systems** . In *Proceedings of the International Workshop on Networked embedded and control system technologies: European and Russian R&D cooperation - Volume 1: Workshop NESTER, (ICINCO 2009)* ISBN 978-989-674-004-7, pages 134-145. DOI: 10.5220/0002279101340145

#### in Bibtex Style

@conference{workshop nester09,

author={Alessandro Astilfi and Romeo Ortega and Aneesh Venkatraman},

title={A Globally Exponentially Convergent Immersion and Invariance Speed Observer for n--Degrees of Freedom Mechanical Systems},

booktitle={Proceedings of the International Workshop on Networked embedded and control system technologies: European and Russian R&D cooperation - Volume 1: Workshop NESTER, (ICINCO 2009)},

year={2009},

pages={134-145},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0002279101340145},

isbn={978-989-674-004-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Workshop on Networked embedded and control system technologies: European and Russian R&D cooperation - Volume 1: Workshop NESTER, (ICINCO 2009)

TI - A Globally Exponentially Convergent Immersion and Invariance Speed Observer for n--Degrees of Freedom Mechanical Systems

SN - 978-989-674-004-7

AU - Astilfi A.

AU - Ortega R.

AU - Venkatraman A.

PY - 2009

SP - 134

EP - 145

DO - 10.5220/0002279101340145