On computing the complex passivity radius

Michael L. Overton; Paul Van Dooren

doi:10.1109/CDC.2005.1583449

On computing the complex passivity radius

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We characterize the complex passivity radius of a rational transfer matrix G(s) := C(sI_n -A)^-1 B + D and propose an approach to compute it. The method depends on computing the smallest structured indefinite perturbation to a Hermitian matrix that makes it singular. We consider both additive and multiplicative perturbations, giving details for the additive case. In both cases, the smallest indefinite perturbation can be efficiently computed by solving a unimodal optimization problem in a real parameter. The passivity radius can be computed by minimizing the smallest singularity-inducing multiplicative indefinite perturbation of a frequency-dependent matrix over the imaginary axis.

Original language	English (US)
Title of host publication	Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Pages	7960-7964
Number of pages	5
DOIs	https://doi.org/10.1109/CDC.2005.1583449
State	Published - 2005
Event	44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 - Seville, Spain Duration: Dec 12 2005 → Dec 15 2005

Publication series

Name	Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Volume	2005

Other

Other	44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Country/Territory	Spain
City	Seville
Period	12/12/05 → 12/15/05

ASJC Scopus subject areas

General Engineering

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10.1109/CDC.2005.1583449

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Overton, M. L., & Van Dooren, P. (2005). On computing the complex passivity radius. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 (pp. 7960-7964). Article 1583449 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005). https://doi.org/10.1109/CDC.2005.1583449

On computing the complex passivity radius. / Overton, Michael L.; Van Dooren, Paul.
Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. p. 7960-7964 1583449 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Overton, ML & Van Dooren, P 2005, On computing the complex passivity radius. in Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05., 1583449, Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, vol. 2005, pp. 7960-7964, 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, Seville, Spain, 12/12/05. https://doi.org/10.1109/CDC.2005.1583449

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On computing the complex passivity radius

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