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Automatica
Volume 38, Issue 2, February 2002, Pages 249-259
 
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doi:10.1016/S0005-1098(01)00196-0    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2001 Published by Elsevier Science Ltd. All rights reserved.

Brief Paper

A convex approach to the characterization of the frequency response of ellipsoidal plants*1

G. Chesia, A. GarulliCorresponding Author Contact Information, E-mail The Corresponding Author, a, A. Tesib and A. Vicinoa

a Dipartimento di Ingegneria dell'Informazione, Università di Siena, Via Roma 56, 53100 Siena, Italy b Dipartimento di Sistemi e Informatica, Università di Firenze, Via di S. Marta 3, 50139 Firenze, Italy

Received 11 January 2000;
revised 31 May 2001;
accepted 17 July 2001
Available online 14 December 2001.

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Abstract

This paper deals with the frequency domain properties of an ellipsoidal family of rational functions, i.e. a family of rational functions whose coefficients depend affinely on an ellipsoidal parameter set. The considered problems are relevant to several recently developed techniques in the identification-for-control research area. A complete characterization of the frequency plots of such a family is provided and an efficient algorithm for computing the envelope of the Bode plots is devised. In particular, it is shown that the extremal values of the magnitude and phase of the family frequency response, which in general involve non-convex optimization problems, can be computed via a sequence of simple algebraic tests.

Author Keywords: Identification for control; Parametric uncertainty; Frequency response; Convexification techniques

Article Outline

1. Introduction
2. Problem formulation
3. Characterization of the value set
3.1. Computation of Image (full rank)
3.2. Computation of Image and Image (loss of rank)
4. Computation of the extremes of the value set
5. Examples
6. Conclusions
Appendix A
A.1. Proof of Lemma 1
A.2. Proof of Lemma 2
A.3. Proof of Lemma 4
A.4. Proof of Lemma 5
A.5. Proof of Lemma 6
A.6. Proof of Lemma 7
References
Vitae





Automatica
Volume 38, Issue 2, February 2002, Pages 249-259
 
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